I was wondering if there is some way to arrange so that if my opponent makes a chess move X next go and I have already decided that I would respond to that move by doing Y move, rather than he having to wait for me to do Y move, the Y move would be done automatically if he does move X? I assume that is what is meant by “conditional moves”?
I tried clicking on “con. move queue” and also “Conditional moves” but neither tells me how I can set this up.

Your understanding about conditional moves is correct. What you need to do is:

Click 'Conditional moves'.

On the board which appears, make the move you are expecting from your opponent and then make your move in reply.

Click on the button for 'Submit conditional move'.

Originally posted by C J Horse
Your understanding about conditional moves is correct. What you need to do is:

Click 'Conditional moves'.

On the board which appears, make the move you are expecting from your opponent and then make your move in reply.

Click on the button for 'Submit conditional move'.