You can start a PvP match by tapping / clicking on the central button with the two crossed "swords".
Once a PvP match starts, you are presented with usual Booty Calls game board, but, with extra PvP elements.
Each player will have their turn to make a move. The better matches you make, the more score you get.
Here's where the power up progression comes in handy. Leveling color perks will increase the score by quite a lot.
As seen in the above screenshot, each player has 6 turns of 20 seconds each. Once your turn starts, each second is visibly counted in the small circle next to the users' profile. When a second passes, the purple color fills up with cyan, until it completely fills and the time is up.
If you run out of time, unfortunately, your turn will be lost.
The bar between the two player profiles is where you can see the score and keep track of it.