First, when is a good time to start learning to loop? Personally, I think you can start almost immediately. Don't feel like you have to be good at string tricks before you move to looping, or vice versa. Doing more than one thing at once can help to alleviate boredom, and I think actually can improve your skills at both, like cross-training.
Once you've gotten to the point that you're comfortable with simple stuff like the Throwdown, Forward Pass, Sleeper, Around the World, etc. I think you are ready to start.
Note: However, it may be worth knowing a string tension trick such as Flying Saucer/UFO/Sleeping Beauty. Loops effect your string tension, and being able to compensate without letting your string hang down will be less of a hassle.
Now, your choice of yo-yo is important. I would like to steer someone who is learning away from transaxles and butterfly yo-yos. A fixed axle imperial yo-yo is usually ideal. A butterfly will tend to "lean over" much more easily, and be generally hard to control. A transaxle will be more likely to "stall" at the end of the string, making it hard to wind up the string during each loop. Some transaxles can loop fairly well, but you'll have less to worry about with a fixed axle, especially when you are starting out.
Some personal recommandations are Technics, BC/What's Next yo-yos (Spitfires, Phantoms, Rainbows), No Jive 3-in-1, Da Bombs (with wooden axles), ProYo2, Pamela, Russels, Duncan Professional, and many others. Don't feel limited to this, but that should give you an idea on what to look for.
For string I'd recommend some normal width Type 8 string. Type 6 (thiner) is a bit fragile for looping and will tend to loop up. Type 10 might loop down. More information on this below.
Also, check to see that the string is a good length. Some people prefer looping with a string that is slightly shorter than usual. Experiment to find a comfortable length.
Now that your skills and yo-yos are in place, here is some more information on how loops work.
Loops put a great deal of strain on both the string and your finger. While you will get a callus on your finger eventually, if you do a great deal of loops, even that may not be enough to protect you. I think if you're going to do a great number of loops, you should use some sort of protection.
Some people use bandaids. That is allright, but for some the string will slip off, and it'll leave residue. Personally I use Sports Tape that you can get from a drugstore or sports place. Generally they come in rolls at a good price, come off easy without mess, and are cushiony enough to keep the string on. Yomega also has some special self-sticking tape (which is similar to what can be found in a drugstore, but at the right width and in lots colors).
A lot of factors are at work in loops. Motions, spinning, tilting, flipping. I'll try to sort out some of it here, and how it effects your loops.
In the simplist form, a loop starts with a forward pass. As the yo-yo comes back towards your hand, you twist your wrist and fingers, sending the yo-yo back out. You can catch the yo-yo with your palm up, or continue to loop as long as you can.
The yo-yo makes an oval-shaped arc, and this is what most people see when you loop. But there are many things that are not as easy to see.
The biggest thing is that the yo-yo actually flips over ever time the yo-yo reaches your hand and gets thrown back out.
In order to see this effect, you can take two take-apart yo-yos with different colors and make a mixed color yo-yo. Now, you should see that the colors switch with every loop.
This is part of the reason why a butterfly yo-yo is harder to loop. With all the mass on the rim of the yo-yo it tends to want to stay straight, and not to flip over. So generally the more weight there is in the center of the yo-yo, the easier it is to control. Yo-yos like the Spitfire are shaped the way they are, to give more weight to the center and be easier to loop. A yo-yo like a Technic, while still being a good looping yo-yo, will be slightly harder to control due to there being more weight at the rim.
This flip is a half a turn, and the direction of the flip generally depends on what hand you are looping with. This effects your string, since the flipping will cause your string to wind looser or tigher a half-turn every time you loop. This may not be obvious at first, but when you start looping 50+ times in a row, it will become very apparant.
Inside loops with your right hand will make the string looser. Inside loops will make the string tighter. Other kinds of loops are effected in other ways, which I will mention in their respective sections.
Note: It IS possible to loop without the yo-yo flipping each time. However it is difficult to control and usually happens by mistake. If you are looping, especially doing a transition, and the yo-yo suddenly seems to speed up and feel totally different, then it may be looping without flipping. This sort of thing is more common with hop the fence, where it is somewhat easier to control. But while it is interesting and has certain possibilities, I would discourage anyone from getting into the habit of looping this way, since it is so hard to control and doesn't seem to have any huge apparant benifits.
I mentioned before that the thickness of the string effected the height of your loops. This is true, but it would be more correct to say that the ratio of gap width to string width is what effects height. If the gap of the yo-yo is large in comparison to the string, then the yo-yo will loop up. If the gap is small, then it'll loop down.
Many advanced looping people will take a narrow-gapped wooden yo-yo, and sand the gap until it is wide enough to their liking. A yo-yo with an adjustable gap like a da bomb lets you adjust things a bit. But generally a regular yo-yo with Type 8 string will work well.
Note: If you are using a plastic Duncan yo-yo, I would be very carefull. I have a Professional that loops great, but I've seen ones with gaps so small they loop almost straight down and have barely enough room to wind the string. On the opposite side, after a lot of use, many of them will start to come apart and loop up. Many wooden yo-yos also have this problem of falling apart after a while. If either of these things happens, it isn't your fault. Just pull it apart and glue it at a better width (but don't get glue on the axle where the string will touch).
Lastly, it is important to know about the angle of the yo-yo. When a lot of people start looping, they assume that the yo-yo should be straight up and down. However, due to the way loops work, they tend to settle into an angle of least resistance. Sometimes this is called the Control Angle.
Generally when looping with your right hand, you'll want the angle at about a 1 o'clock angle. For left-handed it'd be at about an 11 o'clock angle.
Note: Those angles are the ones that are generally used, but it is important to know that the angle of the yo-yo is related to the angle that you move your wrist. While the yo-yo is tilted, your wrist motion should be straight up and down. It is possible to tilt both your wrist and the yo-yo and remain in control, but this will be covered in a later section.
Ok, now you have the yo-yo, the string, and the knowledge of how loops work. It is time to get started. I'm just going to give some tips that I found helpfull, and may help you out.
One of the most important things when you loop is the throw, and is often overlooked. In order to do a bunch of loops, you need to start out right. Messing up a throw is like trying to win a running racer after tripping at the starting gate.
I'd recommend throwing at a level height. A little below eye level usually works well. It may be easier at first to throw a little bit to the side. A bit to the right for a righty, a bit to the left for a lefty. This is optional, and when you get more used to looping, you'll want to try to loop straight in front of you.
Lastly, I'd recommend throwing the yo-yo out at the angle you're going to loop at. This way when you start to loop, it is already angled and ready. Then you can just use a straight looping motion, and should be all set.
One thing that many people do when they start to loop is to move their whole arm around in a circle. You want to try to minimize this as much as possible. Try to keep your arm as still as possible and move your wrist and fingers.
The motion varies from person to person slightly, but I do it this way. After the yo-yo is thrown and is out in the air, I keep my hand in a "handshake" position with my fingers out and palm pointed to the side.
As the yo-yo starts to get back near my hand, I twist my wrist so my palm is facing somewhat towards me and bend my fingers so my middle finger is near my palm and wrist. Then as the yo-yo goes around, I turn my wrist back and extend my fingers back out. It smooth "flicking" motion, as if you were trying to swat something.
Remember that the only part of your hand that the yo-yo really cares about is where the string is connected to it. Where the slipknot is on your finger. You want this spot on your finger to make a circular motion, but at the same time that circle needs stay in a straight plane. It should go straight up and down, straight away and towards you, and not to the left or right at all.
Lastly, timing is very important in loops. Don't wait until the yo-yo hits you in the hand before you start to loop. You'll want to start to pull it around when it is still a little ways from your hand, and then throw it back out, so it is all a smooth motion. This is something you'll have to experiment with until you find something that is comfortable.
As for overall speed, don't worry about doing fast loops until you are doing well. Just take your time. It is much more important to have a consistant rhythm then a fast one.
I think that covers most of the aspects of inside loops. Here is some miscellaneous tips and advice for when things go wrong.
One piece of advice that everyone seems to come up with is "Only Practice Good Loops". When loops are going well, you can usually tell. Generally it is better to start small and work your way up. If the yo-yo starts to goes out of control, stop and try it again from the beginning. The reason being that you want to practice the good loops and not let yourself get into bad habits. Also, it forces you to get smoother loops instead of flailing around after the yo-yo.
However, control is a big aspect of looping, and knowing how to correct mistakes is important. It is good to experiment when things go wrong, but work on getting control of the loops back. Don't just work on how to do a lot of barely controlled loops.
Don't under-estimate the stamina issue. It will take you a while before your hand simply gets the strength to do more than a certain amount of loops at a time.
Relating to the string tension issue, don't be afraid to double-loop a fixed axle yo-yo to help with learning. This will keep the yo-yo responsive even as the string tension changes. You'll still have to adjust it after a while, but won't have to do flying saucer every minute.
This can be of immeasurable help, especially in taking out some of the initial frustration. I did this myself, and found there wasn't any trouble when I switched back to single-looped for my looping.
I find something that helps to keep my loops consistant is if I do a good loop, to see the point in the background (like a spot on a wall in front of me or something) where the yo-yo was when it was fully extended. Then try to throw the next loop so it goes out to exactly the same spot. If your arm stays in the same spot, and the yo-yo goes out to the same spot, everything should be consistant.
One of the biggest problems when you start to loop is that the angle on the yo-yo slowly changes with every loop until the yo-yo goes sideways and you loose control.
This is a difficult thing to address, and something that will take a lot of practice to take care of. Here are my main recommendations.
Look at your wrist/finger motion. Try to make sure that everything is straight. If your motion is tilted at all, then the yo-yo will also tilt. Look at your timing. Try to start your motion soon or later in relation to how close the yo-yo is to your hand. Make sure your forward pass is tilted the right way. All of those things contribute.
The 1/11 o'clock angles are the standard, with some leway either direction. Once it passes the leway point, the yo-yo will go out of control. If you are doing well with looping, and for one reason or another it decides to tilt, it is possible to compensate before control is lost. You can "nudge" the angle back up by angling your wrist motion.
What happens is that for your wrist motion, the yo-yo settles into an angle that is the least resistance. Between the angle of least resistance, and then end of your leway that you can keep control, is the "nudge zone". If you tilt the wrist motion a little bit, but not enough that you loose control, and keep looping that way, the yo-yo will tilt to the angle of least resistance for that motion.
I "think" what happens sometimes for the for the yo-yo falling on the side, is that the wrist motion tilts without you knowing it, which slowly nudges the yo-yo sideways. Then you notice, and try to compensate by looping straight, but by then it has already passed the leway zone of a "straight" loop and so it goes out of control at that moment.
It is possible to start looping sideways and then nudge it back up, but that takes a lot of control, and best to wait until you have straight loops down, or else you risk getting in the habit of always tilting and having to correct yourself...
But as I mentioned above, the angles are also effected by things like timing, strength of your wrist, length of string, and various factors. The biggest peice of advice I can give to you is to just keep practicing and not give up!