A game against another player is played in turns, at your own pace: you play your turn whenever you like, then your opponent plays theirs, sometimes a few minutes later, sometimes the next day. The site tells you by email when it is your turn. For how to play a turn (shooting, movement, combat), see the Against the AI tutorial: it is exactly the same screen. The screenshots come from the French version of the site.
Go to the Play page, then click Create a new game. Choose the scenario, the deployment and the melee table, then click Human (framed in orange). A few settings appear:
Click Create the game. It now waits for an opponent.

Games waiting for an opponent are listed on the Play page. Each card shows the scenario, the creator and their reputation, the time per turn, the side still free and the melee table. Click Join to take the free seat.

If you created the game, you get an email as soon as someone joins it. You also find all your current games on your dashboard.
While your opponent plays, you can open the game and look at the map, but not play. The pink banner under the title tells you where they are: the current phase (shooting, movement or combat) and the side playing.
The screen does not update by itself. To see whether your opponent has finished, click Refresh, at the top left, or simply wait for their email.

The site writes to your account's address:
Not getting anything? Check your spam folder (junk mail, Promotions tab…). If an email from the site is there, mark it as "not spam" or add the sender to your contacts: the next ones will reach your normal inbox.
When you open the game and it is your turn, a replay first shows you everything your opponent did: their shots, their moves, their infiltration tests, their combats, with the dice rolling. The replay buttons are described in the Against the AI tutorial. Click the red square to stop the replay, then play your turn.
When you end your combat phase, the turn passes to your opponent: they get an email in turn, and you are the one waiting.

Do not keep your opponent waiting too long: if your time per turn runs out, they can claim victory, and your reputation goes down.