I'm proud to say I've never made a stringy fondue myself, but the credit goes to my Swiss instructor. The basic caution is to not use too high a heat while cooking it or on the rechaud. Apparently this is what can turn a good fondue into a stringy mess.

On the stove, don't go above medium-high, and stir constantly. Once it's ready to eat, remove it to the rechaud. Adjust the heat source of the rechaud so it's only lightly bubbling; the idea is to keep it warm, but not cook it any further.

Hope this helps, and good luck!!

(PS-not everyone adds cornstarch, (maizena) to their fondue, but I like to add some--dissolved in kirsch or wine--to make it thicker and smoother.)