Transit hotels(3 in Changi) are always full. You either book many weeks in advance, or hope for cancellation. I have always been able to get something by ~11pm without reservation.

There are several pay-in lounges you can use overnight (SATS premier, Rainforest, Ambassador). One of the SATS has cradle chairs you can sleep in. Rainforest has some kind of day bed(but costs more than transit hotel).

Without paying, you can use one of the the open area lounging chairs, or the free movie theatre.