You can use a Forstner bit in a hand-drill, but you should use a drill press. Hand-drills are less accurate, and you might end up with the hole not being level. Drill presses are easier because you can set the depth and the angle and forget about it while you make multiple holes.
When drilling through wood to create the initial hole, the Forstner bit has a pointed middle that acts like a pilot to hold the wider body of the bit in the center of the hole. If you are trying to widen an existing hole, there is no way of stopping the bit from wandering because the center point has nothing to grip on to.