Just as with the Tricep Extension, it is very important to keep your wrists cocked when doing the Barbell Curl. Form a cup with your wrists, allow the bar to set into the cup and do not let the wrists break at any time during the movement.
Keep your elbows in tight at the side and do not cheat by swinging back and forth -- this is a bicep exercise, not a back exercise.
Progressively increase the weight over time, as long as you maintain good form, and your biceps will grow!
Train hard!