This is what I do:
Bicep Barbell Curls 3x10
Incline Curls 3x10
Preacher Curls 3x10
Reverse Preacher Curls 3x10
Hammer Curls (with a rope usually) 3x10
From what I know, this works out all the muscles that make up your bicep; biceps brachii, and the brachialis.
Biceps brachii consists of two muscles, short head, which is the part of the bicep that is closer to you, and the long head, which is on the other side, facing further away.
The brachialis, which is sometimes overlooked, is underneath the biceps brachii.
For optimal results, you should try to tighten your triceps when your arm is straight down (that is when the bicep is completely compressed).
I also focus more on negative movement (when the weight is being brought down) than positive (when the weight is going up).
Hopefully this helps.