chain drops happen most often when you try to do it on an uphill, since you're applying so much force to the pedals.

to shift gears when stopped, try this:

hold down the front wheel's brake (left hand)
shift one or two gears (right hand)
tip the bike forward so the rear tire is off the ground and rotate the pedals one revolution (right leg)


other than that, as others have said, shift up to an easy gear before the incline. you can always downshift if it's too easy.