In a serious game, what you do when it's your turn is stop (pause) the clock. If it's not your clock and you don't know how, before the game starts, ask how to stop it just in case.
With the clock stopped, make your claim e.g. you'd say "draw by repetition." If your opponent and you do not agree, then you should leave the board and find an arbiter or tournament director. Be sure to know the rules as there are specific procedures. In the US you write down your move, but you don't play it. The same for the 50 move rule.
If there is a repetation (which takes place more than thrice) involving 3 (or more) moves (instead of 2), there are some players who do not accept a draw, if they have time advantage. Is this legal? Is it possible to claim a draw in this these situations? (I have no experience of an actual tournament, so would like to know how is this kind of situation dealt with, in more serious games). Any comments or discussion about this is welcome.