A booking paid by card confirms itself the moment the payment lands. You only answer the bookings that wait for you:

No price for that length: the athlete requested the slot and nothing was charged.
Pay at the session: the athlete pays you directly when you meet, nothing is charged online.
Payment in progress: the athlete has started paying. Give it a few minutes: if the payment lands, the booking confirms itself.

How to answer

Open the Calendar. A banner shows your pending requests; press Review, or tap the booking.
Read the note under Awaiting your confirmation, then press Accept or Decline.
When you decline, you can add a reason. The athlete sees it.

Requests for today also appear on your Dashboard in Today's focus, with Confirm and Decline.

What happens next

The athlete is told either way. Someone without a Fitiva account is not, so the app reminds you to tell them yourself.
For a pay-at-the-session booking, press Mark as paid once you have the money.
If you decline while a card payment is still in progress and it arrives afterwards, it is refunded automatically.
A request from someone new also appears on Athletes as a new athlete from Fitiva. Until you take them on or decline them there, the request holds a seat on your plan's athlete limit.
Ava can accept or decline a request when you ask. You confirm first.