After you accepted their request, you should have gotten a "Confirmed! So and so will be arriving on such and such date!" at the top of the message chain. That seems to suffice as a confirmation. And then you occasionally get a reservation reminder prior to the guest's arrival.
There is no formal check in. That is, you do not click anywhere once the guest arrives. I think the first time, I got a message "how did so and so's arrival go?", but not since then.
Payment arrives approximately 24 hours after check in. You will get a message that a payout of $x has been sent. In my experience it is a bit less than 24 hours. I think usually it is by the next mid-morning (when technically my checkin is at 3:00 PM).
Good luck!