You can pre-record your next move, if you know what your opponent's move is going to be. Only you can see the conditional moves that you create. If your opponent makes the expected next move, your pre-recorded move is automatically made for you. If he doesn't, your pre-recorded move disappears unused and the game proceeds just as if no conditional move was ever pre-recorded.
In Quick Mode, if your opponent has 2 or 3 possible moves, you can pre-record your response to each of these possible moves individually. In this situation, your Conditional Moves page will show "3 conditions queued" or some such. The only conditional move which will take effect is the one related to the move your opponent actually makes.
That's the basic process for Quick Mode, which is the default on the Conditional Move page. Deep Mode allows a series of moves, but I can't describe it as I've never used it.
You can only record conditional moves when it is your opponent's turn to move. I submit my actual move, then open the game again and "conditional moves" will appear as an option in the list.