PvP in Grow and Conquer is asynchronous. You attack the defense setup of another player.
When you search for a match, you are looking for a target. Check their Castle Level and their Defense Rating. Do not bite off more than you can chew.
If you win, you steal a percentage of their uncollected Gold. It is a brutal tax on the weak.
But remember: if you attack, you leave your own shields down. Be ready for retaliation.