Hammer Curl is the best exercise for developing brachioradialis (the big forearm muscle that will be facing up as you perform this exercise) and a great wrist friendly exercise variation targeting biceps.  Holding dumbbells with thumbs up and palms in alleviates stress on wrist tendons and reduces risk of injury.

To perform the hammer curl you first need to establish a solid base.  Place your feet at shoulder length (adjusting to comfort, narrower or wider).  You could keep your feet straight, or introduce a minor bend in the knees.  Keeping a slight bend in the knees helps absorb any balance adjustments as you perform each set.  This could help you avoid rocking back and forth.  Don’t push up from your feet if you decide to introduce the bend into your workout. Form a block with your upper body.  Hold your back and shoulders straight and chest out (you can stand next to a wall to help maintain good exercise posture).  Press your upper arms into your body to stabilize them.

Lift the weight by flexing your biceps.  Do not swing the weight, raise your shoulders, or bring the elbows up.  This is an isolation exercise – the movement should be limited to your elbow.  

You can do hammer curls by alternating arms, at each rep, each set, or lifting both at the same time.