Can I hold a flight seat for my customer while they make up their mind, or do I have to take payment straight away?

Yes on some flights, but not on all of them, and it is the airline rather than us that decides.

Where an airline allows a seat to be held without payment, the booking is created and the airline returns a reference along with a deadline by which the ticket has to be issued. When the supplier passes that deadline through, your staff can see it on the booking in your portal, so they know how long they have. If nobody issues the ticket before the deadline, the airline normally cancels the hold by itself and the seat goes back on sale, often with no warning to you.

Budget airlines mostly do not offer holds at all. With those, the fare is only secured once the payment has gone through, so what your customer sees in the search results is really just a quote until the ticket is issued. Full service airlines booked through a global distribution system are more likely to allow a hold, although the time allowed can be very short, and on the cheapest fare types or on flights departing soon they may refuse it. A hold does not always protect the fare either, because some airlines reprice at the moment of ticketing.

The sensible next step is to ask us which of the flight sources on your portal allow holds and whether that is included in your plan, then make sure your staff read the ticketing deadline on each booking and tell the customer clearly that an unpaid hold is not yet a confirmed ticket.