Chocolate needs to be moderately soft in order to curl without breaking or flattening. A small block of chocolate can be softened by placing it under a lamp or in a microwave using 3-second bursts on high power. It usually takes a few tries to get the chocolate soft enough without oversoftening it, but once this point is reached, it will hold for at least 10 minutes, giving you enough time to make lots of beautiful curls.
I find the best utensil with which to make the curls is a sharp vegetable peeler. Hold it against the upper edge of the chocolate block and dig in the upper edge of the cutter, pulling it toward you. Increase pressure to form thicker, more open curls. Decrease pressure to make tighter curls. Until the chocolate is sufficiently warmed, it will splinter. When it becomes too warm, it will come off the block in strips that will not curl. But if the strips are not too soft, you can use your fingers to shape the curls. Keep your fingers cool by periodically dipping them in ice water and drying them well.