White Hat pretty much covered it. If the kick is touched by R (the receiving team) first and the touching happened past the line of scrimmage, then whomever has possession of the ball at the end of the down gets a new series of downs.
The only way K (the kicking team) can get a first down if the kick ISN'T touched by R beyond the LOS is if K:
a.) recovers the kick BEHIND their LOS, and
b.) gains enough yards to reach the line to gain
Some other notes on K and kicks:
1.) First, the important definition of what "kick" means: at the high school level (I can't speak for the higher levels) it is the status of the ball from the time the ball is struck by the foot or lower leg and lasts until the ball is possessed by someone. So you could have all 22 players on the field TOUCH the kick and it would still be a kick until someone actually possesses it. Wherever you hear or see an official use the word "kick", this is the timeframe they are talking about.
2.) Any touching of the kick by R behind the LOS is ignored.
3.) K cannot ever advance a kick they recover beyond their LOS. Once they gain possession beyond the LOS, the ball is dead and gets awarded to K or R depending on whether R touched the ball first.
4.) ANY kick that crosses R's goal line is a touchback unless K touched the kick sometime prior to the touchback (in that case, R can take the ball where K touched it, or take the touchback). It doesn't matter whether R muffed the kick first. This is different from the NCAA and NFL and the lack of knowledge about this difference creates unnecessary grief from the players, coaches, and stands.
This post was edited on 10/31 1:06 PM by Fadamor