Make sure there is fuel in the gas tank of the skid steer. Running out of gas will certainly make the skid steer not run. If the gas is empty or extremely low, add fuel to the tank.
Inspect the exhaust pipe. Dirt or debris can easily clog up the exhaust pipe, especially if the skid steer is used in a muddy field. If the exhaust is clogged with mud, bend a wire coat hanger to shape and use it to remove the dirt clog from the exhaust pipe.
Access the engine compartment and remove the air filter cover. Check the air filter. If it is dirty or corroded, replace it with a new one.
Follow the fuel line running from the gas tank to the carburetor on the skid steer to locate the inline fuel filter. Use a wench to remove the filter. Replace it if it looks dirty.