What happens if you don't hit the chess clock?

So, in a serious game, what happens when a person makes a move but doesn't hit the chess clock? Does the time just run out or will an arbiter come to hit the chess clock for them? 

When they run out of time you win by time forfeit.  The times that has happened to me in OTB play, I let the opponent know to hit the clock.

It is against the rules for anyone to let someone know to punch their clock.

In practice, one of two things generally happen. The other player will indicate that the clock needs to be hit, or the player will take the time they normally would on the move, make their move and hit the clock, even though it doesn't do anything.

Officially the move isn't completed until the clock is hit, so the opponent doesn't have to move or notify the player of that fact, but most players, in my experience, will do one of the things I mentioned.

FIDE Laws of Chess:
6.7 a. During the game each player, having made his move on the chessboard, shall stop
his own clock and start his opponent’s clock. A player must always be allowed to
stop his clock. His move is not considered to have been completed until he has done
so, unless the move that was made ends the game. (See the Articles 5.1.a, 5.2.a,
5.2.b, 5.2.c and 9.6)
https://www.fide.com/FIDE/handbook/LawsOfChess.pdf 
So as long as a player has not hit the chess clock, his move has not been completed, his time runs out and he loses the game.

#6
Checkmate on the board prevails over a fallen flag. The opponent has to claim flagfall before the checkmate or stalemate is delivered.
6.8 A flag is considered to have fallen when the arbiter observes the fact or when either
player has made a valid claim to that effect 
5.1 a. The game is won by the player who has checkmated his opponent’s king. This
immediately ends the game, provided that the move producing the checkmate
position was a legal move.

9.1 a. The rules of a competition may specify that players cannot agree to a draw,
whether in less than a specified number of moves or at all, without the consent of
the arbiter.
b. If the rules of a competition allow a draw agreement the following apply:
(1) A player wishing to offer a draw shall do so after having made a move on the
chessboard and before stopping his clock and starting the opponent’s clock
So if a player has made his move but did not hit the clock, he might be contemplating to offer a draw.

I made such a mistake in a local league game by pointing at his clock (my team colleague who was down to  couple of minutes against an opponent with 15mins +).  I got a dirty look and told that's now allowed and I wasn't aware of these rules (are we not gentlemen etc?).  

So two things I'm not clear on...

1.  As it isn't the players fault I pointed it out (and like I said I wasn't playing), surely I should get the blame (not sure what/how) or would the game be considered a forefeit?

2.  So if a player's move, is only complete when they hit the clock, does that mean if your opponent makes his move this is out of turn etc??

Then your time will keep draining

And your opponent might remind you

The arbiter will come to hit the chess clock for them. If a player does not hit the chess clock and their allotted time runs out, they will forfeit the game. In some tournaments, this may result in a penalty or loss of points.