Ever bring home a riding mower and find that it isn't going to even try to start?
Check to see if the battery is fully charged.
Then you need to figure out if it is mechanical or electrical.
Does it grunt, or just do nothing at all?

Is there a certain set of things that have to be just so before starting? Sitting on the seat, having the blade disengaged, being in neutral, and having the clutch in are normal requirements.  Maybe the previous owner knows what those requirements are if you didn't get a manual.

If that's not it and the battery is good:

If it grunts, it may have gas or oil in the cylinder and you could check that by pulling the sparkplugs and trying to crank it.  If it is still grunting with the plugs out, then it may be the starter.  If the engine is locked up solid after the plugs are out, you may have made a very poor purchase.

If it does nothing at all, you want to check the circuit to the starter and see if electricity is getting to the starter terminal. Sometimes the switch or solenoid are bad. Usually though it's one of the three or so safety switches.
There's usually a seat switch, a neutral or clutch switch and a deck or blade engaged switch. If any of those are out they cut out the starter circuit.  A lot of times the deck will get wonked putting a mower in the truck or on the trailer and the mower thinks you're trying to start with the blade engaged.