The honest answer is between a day and a week, and the reason nobody can be more precise is that drying time is set by thickness, humidity and airflow rather than by the clock. A thin coaster is dry overnight. A solid modelled figure two centimetres through can still be wet in the middle after five days, and will crack if you hurry it.
What actually controls the time
Water leaves a clay body from the surface, and the rate depends on how much surface there is relative to volume, how dry the air is and how much of it is moving. That is why a thin slab dries in hours and a thick solid form takes days: the water in the middle has to travel to the surface before it can evaporate at all. Room temperature matters far less than airflow, which is why a fan in the room does more than a radiator under the piece.
How to tell when it is genuinely dry
Touch the piece to the back of your hand. Damp clay feels cool because evaporation is still taking heat out of it, and a piece that has stopped feeling cool has stopped losing water. Colour helps as well: most bodies lighten noticeably as they dry, and a darker patch is a wet patch. Both tests read the surface, so on anything thick, wait a day past the point where it seems ready.
Drying evenly is the whole technique
Cracks are almost never caused by drying too long. They are caused by one part drying faster than the part attached to it, so the shrinking edge tears away from the still-full-size middle. The fix is to slow the fast parts down rather than to speed the slow ones up: cover the piece loosely with a plastic bag for the first day, turn it so the underside gets the same air as the top, and keep it off a radiator and out of direct sun.
Where thickness comes in before drying does
If a piece is thicker than about two centimetres anywhere, hollow it out before you start drying, exactly as you would with a body destined for a kiln. A hollowed form dries from both surfaces and halves the distance the water has to travel. This is one of the few places where a technique borrowed from fired pottery applies unchanged to a material that is never fired.
Questions people ask about air dry clay
How long does air dry clay take to dry?
One to three days for something thin, up to a week for something thick, at ordinary room temperature with air moving in the room. Thickness matters more than any other variable.
How can I tell if it is dry all the way through?
It stops feeling cool against the back of your hand and the colour is even with no darker patches. Both tests read the surface, so on thick pieces wait an extra day.
Does a warm room make it dry faster?
A little, and moving air makes more difference. Neither is worth using aggressively, because uneven drying is what cracks a piece.