Keep your elbows pointed down. Alot of people make the mistake of swinging the weight up a bit so the elbows point forward a bit. This takes pressure off the biceps and puts it on the front delts. Your forearms should be the only parts bending. Keep arms close to your side and at the top of the lift, flex the bicep, dont just hold the weight up.
assuming your gym has mirrors, stand next to one (not facing it) and as you curl, watch your self from the side. make sure nothing but your forearms are moving. and especially make sure you aren't using your back to swing the weights up. you want your biceps and only your biceps to be doing the work. and as said, flex at the top of the rep, then *slowly* return all the way down, then repeat.
If you've been doing it some other way, and are used to it that way, you might need to lower the weight some when you start doing it the right way. Almost everyone screws up their technique on their own (comin here to ask bout it is the right thing to do). When I first started doing it my way, then realized my mistakes, I had to lower my weight, which was discouraging. But in the end, it's better for gains and saving yourself from injury. biggest mistakes I see in the gym are people going too fast, and people only returning like not even half way then going up for another rep.