Your body should remain fixed and only your biceps and forearms should be used to move the weight.
Another mistake is not keeping the elbows fixed and in at the sides. You should not let your elbows come forward when moving the weight up.
And finally, you need to control the weight throughout the set. This means not letting it drop quickly!
Instructions
Grasp a barbell or Olympic bar at around shoulder width apart using a reverse grip (palms facing down).
Stand straight up, feet together (you may be more comfortable putting one foot back for stability), back straight, and with your arms fully extended. The bar should not be touching your body.
Keeping your eyes facing forwards, elbows tucked in at your sides, and your body completely still, slowly curl the bar up.
Squeeze your forearms hard at the top of the movement, and then slowly lower it back to the starting position.