Standing Barbell Curl
Hold the bar with your palms facing out, curl the bar slowly up until it touches your chest, slowly lower down again.
Remember not to cheat as you curl the weight as this takes the emphasis off your biceps and onto your waist, the point is to work the biceps and slow deliberate curls are the trick.
Variations include machine curls or preacher curls.
Standing Alternate Dumbbell Curl
Hold a dumbbell in each hand, curl one up to your chest and lower it, then curl the other up and lower that one. Repeat.
The point of alternate curls is to focus on each arm separately and to also give the other arm a slight rest before you repeat again.
Variations include holding the dumbbell with your palms facing toward your body and keeping them there throughout the movement.
Seated Alternate Dumbbell Curl
Same as standing alternate curls except you are seated on a bench, perform the movement just as you would standing.
Sit on a bench, hold a dumbbell in one hand between your legs with that elbow resting against your inner leg and hold on to your knee with the other hand. Slowly curl the weight in your hand up to your chest and lower slowly.
This exercise is great to really squeeze your biceps at the top of the movement.
Repeat for the other hand.
Alternates to the exercises described here are those done with cables. The can be switched with any of the exercises I mentioned here.