... is the most commonly used material in yoyo string making. This is what the vast majority of commercial string makers use. It is fairly soft, easy to work with and much more durable than cotton. Traditionally "overlocker" style thread has been used, but "trilobal" is gaining in popularity.
Polyester is a great material because it comes in a very wide range of, including neon, colors as well as many different textures. Poly gives you lots of room to experiment if that is your thing. It can also be very inexpensive.
You should be able to pick up polyester thread just about anywhere that sells normal sewing thread.
... is a much less common material in yoyo strings. That said, this is our material of choice because we believe it has some major advantages over polyester. It can be softer, is almost always more durable, and is definitely slicker. Nylon often has more bounce/liveliness to it than polyester as well. Here at Airetic, we enjoy playing with and spinning Nylon strings.
Generally speaking, we use some sort of "wooly" nylon, but some folks use "bonded" nylon. Bonded is much rougher, but if durability is of utmost importance to you, it is as good as it gets.
Nylon colors tend to be richer than poly, but finding extremely bright colors can be difficult. Nylon also tends to be much more expensive than poly thread.
Nylon is usually a little more difficult to obtain than poly as well. It can be found in several places online, but you'll probably find that local selection is limited.
...is, for the most part only used with fixed axle
yoyos. This is due to cotton being more tolerant to the heat build up at the axle on a fixie. Outside of fixed axles, and some looping play, very few people use cotton strings because they do not last very long.
You should be able to find cotton thread fairly easily at your local retailer.
...like rayon, silk, and kevlar are also occasionally used. Each of them has their own specific properties and are generally used to impart some of that property onto a string. Rarely are any of these used as a primary material for yoyo strings. Think of these as "enhancement" materials.
Of course, being exotics, these will both be harder to find and more expensive.