Advice on castling

this maybe a newbie question but want to know this for tournaments that I have been participating in. I know we can usually castle on king's side or queen's side, and that it is recommended that we castle before moving the king, because the king cannot be castled once it has been moved.

The other advice I received was the king should be moved two steps before moving the rook.

So, my question to you guys is do you guys usually use left hand, right hand or both hand to do the castle? Also, how do you tap the clock if you are using both hands?

As far as I know you can only use one hand to do the castle. But I guess it depends on the tournament rules. 

As a USCF Tournament Director, I can confirm you can only pick up one piece at a time with one hand, AND USCF Rule 4 says you have to use the SAME hand (it can be left or right hand) to move the King and the Rook - even in Blitz games!  You always must hit the clock with the hand that made your move on the board (USCF Rule 16C) - though there are special rules for physically disabled players.

You are, by tradition, supposed to move the King first, then the Rook, but there is NO penalty in USCF chess (may be different in other countries) for touching the Rook first, according to USCF Rule 10I2 unless castling is illegal in which case the player must move the Rook if legal.  The guidance to TD's from USCF is to rule liberally on arguments about touching rook first and did the player initially intend to just move the rook and to allow the castling unless it's perfectly clear to the TD that was not the original intent of picking up the rook first.