Board Game Arena

How does one use the "advance" reaction after combat? When I click on the card, it doesn't give me the option to play it . . .

Let be logical, you want to advance what ? A piece, where ? to some location, last step is useless because you advance always in attacked location.
So first, click, on the card, second on the piece (tank or infantry) you want to move.

You have the same logic for retreat with an extra last step: the retreat location.