What are the rules for the onside kick in professional football (NFL)?

As others have stated, pretty much the only rule is that the ball must go 10 yards before the kicking team can touch it. You do not have to announce your intention, it's possible on ANY kick off, it's only usually kicked shorter to make it easier to recover.Based on the added details it looks like you're confusing a Kick-off with a punt. A kick-off is how you initiate play after a score (only touchdowns and field goals, not safeties) or at the beginning of the game and after half time. This it the ONLY time an onside kick is possible. A kick off is usually done as a place kick, where the ball is set on a tee or has someone holding the ball upright. A punt is a play that a team does to concede possession of the ball to the other team in exchange for field position. It usually happens on 4th down, since that's the last opportunity for the team to get a first down. Rather than give up the ball in position, they kick the ball, trying to pin the other team deep in their own territory.On these kicks, the long-snapper snaps the ball about 15 yards to the punter who then drops the ball and kicks it in mid air (not a drop kick).On a punt, the kicking team cannot recover the ball unless it's muffed (the receiving team fails to catch the ball, but it touches a team member). If a member of the kicking team touches the ball first, it's called "improper touching" and the ball is turned over to the receiving team at the place where the ball was touched.  Some other differences -- a kick off cannot be blocked, a punt can. Both can be fair caught (which is why you kick the ball into the ground on an onside kick).There is no such thing as an onside punt.

For a kick off in the NFL the ball is considered live anytime the ball travels more than 10 yards. This means if the kicking team recovers the ball at any point after the 10 yards they are awarded possession of the ball. The kicking team may not advance the recovery the ball is dead at the point they recover. If the ball travels less than 10 yards and neither team touches the ball that is a penalty on the kicker and the receiving team keeps the ball. If the ball travels less than ten yards and the receiving team grabs the ball they may advance the ball. If the ball travels less than 1o yards and the receiving team touches the ball and/or fumbles the ball the ball is then live and the kicking team has an opportunity to recover and  take possession.The onside kick is just a strategy in order to better the odds of the kicking team recovering the ball, because of this the referees do not need to be told that the kicking team wishes to onside kick.