Riding lawnmower turns over but will not start start

Could be several different things causing your problem. As a mechanic i've learned to never assume anyone has checked the obvious. So, since you didn't state what you may have checked:
1: Check to make sure you have gas in the gas tank
2: Check to make sure the spark plug wire is still pluged to the spark plug.
3: Check to make sure the fuel shut off valve on gas line going from tank to engine is in the fully open position. You may even want to remove the fuel line from the tank (putting a bucket below the valve to catch the leaking gas) and observe the flow. If it looks like it is coming out quickly, then I would guess that is not the problem.
4: Check the fuel filter in the same manner as above. Locate the fuel filter and remove the fuel line on the side of the fuel filter that is closer to the engine than gas tank. You should observe a similar fuel flow from the line as from the fuel shut off valve, if not, replace the fuel filter. They are cheap, so can't hurt to replace it if you are in doubt.
5: Check airfilter to be sure that it isn't clogged full causing the engine to draw in to much fuel and flood the engine.
6: Remove sparkplug (usually either a 3/4" socket or 13/16" socket and ratchet will remove it) and inspect the plug. If the spark plug has a lot of black soot between the electrodes then it is fouled out and needs to be cleaned, it could also be bad and need replacing. They are cheap and easy to replace, so in my humble opinion, when in doubt replace the spark plug. If the spark plug has a lot of fuel smell and it is wet, then the plug is either bad or choke is stuck in the closed position (or some call it the on position) or possibly the airfilter is clogged. If you checked the air filter earlier, and it is clean, then check the linkage for the choke to see if it is stuck in the closed or on position. To check it, remove the air filter and look down the large hold in the center and you should see a metal vane in an upright position for the choke to be in the open or off position. If the spark plug isn't fouled out or bad, or its new, and the plug isn't wet, then proceed to #7
7: Now that you have checked all of these simple things, you will need to give more information or take the mower to the local lawnmower shop and have it worked on by a reputable technician.