Put the riding lawnmower on a flat surface before removing its tires. Loosen the bolts on the wheel, but do not remove them. Loosen them using a socket wrench or a ratchet. Sometimes, the bolts are rather difficult to move; having the wheel sit on the ground will allow you to put force into loosening them.
Lift the riding mower. Use your jack to place it underneath the mower, by the wheel that needs to be removed. Lift it high enough for you to comfortably work with the tire.
Place the riding mower into gear. It is best to put it into neutral, so you can easily move the tire without the brake keeping it stationary. Place a brick or block behind two wheels you are not working on, for added stability.
Remove the bolts. Remove the tire from the axle and replace it with a new one. Slide the new tire on the axle and replace the bolts and tighten them. Lower the jack and continue to the front tire.
Place the jack under the mower to lift the front side on which you need to remove the tire. A front tire is a little easier to change than a rear one. There is a cap that sits on the spindle of the tire; remove the cap, and you will see a clamp or something that looks like the letter "C." It is a metal clip that will hold the wheel on. Use a screwdriver to remove it by slipping it underneath the clip and popping it out. The tire can then be removed.
Replace the tire. Slide off the old front tire and replace it with a new one. Slide the new tire on the shaft and replace the clip. There are grooves on the end of the shaft the the clip will fit into. Pop the clip into the groove to hold the tire in place and replace the cap over the end of the spindle.