Look at the side of a tire, near the rim. Find the numbers written on the side. Wash the tire with a mixture of soap and water, scrubbing away dirt with a soft-bristled brush, if necessary, to reveal the numbers.
Write the numbers you see on a piece of paper. There will be three sets of numbers, with the first two sets separated by either an "x" or a "/." If the numbers are separated by an "x," the numbers represent the tire's outer diameter, followed by the tire height -- the thickness of the tire between the top of the rim to the top of the tire -- and the tire diameter. If a "/" is used, the numbers correspond to the tire height, the tire diameter and the rim size. The tire size dictates the tube size, ultimately.
Examine the valve stem protruding from the tire. There are two styles: the TR-13, which features a straight valve, and the TR-87, which is bent at a 90-degree angle. A substyle of the TR-87, the TR-87P, is also bent at a 90-degree angle. However, it runs parallel to the rim and is metal, while the TR-87 is rubber. If you are adding a tube to a tubeless tire, the valve stem style is irrelevant.
Visit a store that sells tubes for lawn mower tires. Provide the sales clerk with the tire information you gathered. The clerk can easily look up the appropriate tube. You can also find information about these tubes online.