I don't play Live much, but I have used 3-fold rep. in Online, and I believe it functions much the same way.
When you are about to make a move that will repeat the position* for the third time, make your move. Once the move is made and before your opponent makes their move**, press the draw button to make a claim. Alternatively, if your opponent has just made a move that repeated a position for the third time, you can press the draw button to claim the draw. If the claim is correctly made, the game will be declared a draw immediately. If not, a draw offer is sent to your opponent which they can react to as they see fit.
* A repetition of position means that the board must look the same at 3 separate times with the same options. I.e., the same player is to move, castling availability is the same, and en passant availability is the same. Note that since en passant is only allowed immediately when available, the "2nd" time a position appears would be different than the first if the option for en passant were available the "1st" time. The actual move that causes the repetition need not be the same as previous times.
**Due to pre-moves (and conditional moves in Online chess), this may not be feasible, since it will be your move again immediately. If their move broke the repetition, then the draw button will offer a draw as usual. Now, if the position after their move is also the third time that position arose, then claiming a draw should still work.
I read through some of the old threads and I am still not entirely clear on how this works in live chess. I am sick of 'losing' games with a repeated position. Can someone walk me through it like I am 4 years old? Does it even work? Can I claim the draw? Do I use the same button as the offer draw, but they don't get a choice to accept? Does it have to be on the third repetition precisely? Please lay it out for me.