You can view which trainers have proposed to your session, by opening the session in 'My Bookings'. Tap on their proposal, and hit confirm session. This only applies to general bookings or if your direct booking has not been confirmed after the first half an hour of sending the request.
Once you direct booking trainer confirms this will complete the booking. If it is a general booking, you will need to choose one of the trainers that have proposed, this can be done by tapping on the proposal and confirming the booking.