If there is black smoke coming from the exhaust of a Toro zero turn radius mower, it usually means that that there is too much fuel in the air-fuel mixture. The engine in the Toro mower needs to correct amount of air and fuel to start or run correctly. The correct mixture should be 14:1.
Check to make sure the choke is full open, if it is then you may have a problem with the carburetor. The choke should be closed when trying to start the mower, but needs to be opened to have it run.
The model and serial numbers on your Toro zero-turn mower can be found on the frame of the mower.
NOTE: if you need a part for the small engine in your Toro zero-turn mower, there will be a separate model/serial number for the engine. Here are the small engines that are available in your Toro mower. Visit the page of the engine you have to find out where the model/serial number is located for your small engine model: