Winding an automatic watch the right way means doing it off your wrist, turning the crown gently in one direction, and stopping once you feel resistance rather than forcing it further. Most automatics don't need manual winding at all if you wear them daily, but a watch that's been sitting for more than a day or two will need a hand to get going again before it'll keep accurate time.
How many turns you actually need
Take the watch off your wrist, unscrew the crown if it's a screw-down type, and pull it out to the first position, not the time-setting position. Turn it clockwise about 20 to 30 turns, or until you feel the mainspring reach tension and the second hand starts sweeping steadily. You're not trying to fully wind it by hand forever, just enough to get it running, since normal wrist motion will take over from there once you put it back on and start moving around.
Stop as soon as you feel resistance increase noticeably. That's the mainspring telling you it's close to fully wound. Continuing to force the crown past that point is the one real way to cause damage while winding, so when in doubt, stop a little early rather than a little late. A slightly under-wound watch just needs more wrist motion, while an over-forced one can strip the mechanism.
Do this off the wrist, not on it
Winding while the watch is still on your wrist puts unnecessary side pressure on the crown and stem, which over years of repetition can wear the mechanism unevenly. Take it off, hold it in your hand, and wind it that way instead. It takes an extra five seconds and saves the crown stem from stress it doesn't need.
Once wound, push the crown back in fully and screw it down if applicable. A properly wound automatic should run for 38 to 70 hours depending on the movement, giving you a buffer even if you skip a day of wearing it.