Some people swear by letting the ball sit overnight after inflation. I call that “the waiting game,” and I hate waiting. But it does help the ball “settle” and adjust to its new, glorious size. If you’re impatient (like me), just use it right away. The worst that can happen is it’ll feel a bit stiff, like you after a long car ride. It’ll loosen up after a few bounces.
Exercise Ball Pump - Fitness Ball Pump with Needle & Nozzle
One more thing: Don’t use your mouth to inflate it. Unless you want to look like a blowfish with lungs of steel, do not attempt this. It’s gross, it’s hard, and you’ll probably pass out before you’re done. Trust the pump—it’s your friend.