Pull the glove onto your dominant hand. Be sure to keep your thumb folded inward to avoid touching the sterile part of the glove. Allow the glove to come uncuffed as you finish inserting your hand, but don't touch the outside of the glove.
Slide your nondominant hand into the glove, holding your dominant thumb as far away as possible to avoid brushing against your arm. Allow the glove to come uncuffed as you finish putting it on, but don't touch the skin side of the cuff with your other gloved hand.