LLX > Neil Parker > String Figures
For most figures, ordinary cotton string works quite well. I find that a nice comfortable loop size is made from a piece of string about seven feet (about 2.1 meters) long, making a loop about 3.5 feet long when the ends are tied together. Children will probably prefer a smaller loop - a reasonable rule of thumb is to cut a piece of string long enough to run from the end of one outstretched arm to the opposite shoulder and back.
Tie the ends of the string together in as compact a knot as you can manage (a square knot works well), and trim off the loose ends. If you know how to splice string, and are willing to take the time, a splice is probably better than a knot. A bit of melted nylon can also be used to join the ends of the string together without a knot (though it goes without saying that that children should not try to melt the nylon themselves - get an adult to do it for you).
For the Nauru figures, the usual cotton loop will not work - a much longer and slipperier string is necessary. The Nauruans made their strings out of their own hair, but most people these days probably won't find that very practical. Nylon string makes a reasonable substitute - I find that that stuff sold in hardware stores as "mason's twine," though a little stiffer than the ideal, works well enough. Cut a piece long enough to stretch from the end of one outstretched arm to the other and back (for me that's about ten feet [about 3 meters]). The ends must be joined by melting - the nylon is too slippery to hold a knot.