According to Wiki:
Under the strict touch-move rules enforced in most tournaments, castling is considered a king move. But under current US Chess Federation rules, a player who intends to castle and touches the rook first would suffer no penalty, and would be permitted to perform castling, provided castling is legal in the position. Still, the correct way to castle is to first move the king.
Typically you move the King first to indicate a castling move, but I don't think it's a hard and fast rule. Certainly not in casual games.
Yes, castling is a king move. Under FIDE rules, you do need to make a rook move once you touched your rook. Apparently USCF changed that, so it doesn't apply in US tournaments.
You must grab the Rook with the pinky and ring finger, then grasp the King with your thumb and index fingers. Then in a casual manner, not to show off or anything, you twist your wrist and make the move. 
Unless your opponent complains about you touching the rook first there will be no problem. If your opponent does complain the TD/Arbiter will most often just warn the player who touched the rook first and not make him move the rook. Its really up to the arbiter .
I played in a tournament a couple of weeks ago against a young boy. It was funny because he moved his King preparing to castle. Then he stopped there and pressed the clock. I had to tell him he forgot to move his Rook.
Unless your opponent complains about you touching the rook first there will be no problem. If your opponent does complain the TD/Arbiter will most often just warn the player who touched the rook first and not make him move the rook. Its really up to the arbiter .
I disagree as the fide handbook is clear on that:
deliberately touches a rook and then his king he is not allowed to castle on that side on that move and the situation shall be governed by Article 4.3.a
4.3
Except as providedin Article 4.2, if the player having the move deliberately touches on the chessboard:
a.
one or more of his own pieces, he must move the first piece touched which can be moved
based on 4.3. and 4.2 the arbiter has no choice than to force the move of rook.
Actually, I know how to castle, all the rules and stuff... But i was playing a chess game with a new neighbor and when I was going to castle he said that i couldn't castle cause i moved the rook first than the king. I only played a few times in a real chess board so i was kinda confused. It is true?