This is a broad topic. Fixing a riding lawn mower can be easy or hard depending on what the problem is. In some cases it may be impossible.
Before you can fix the mower you must determine what is wrong. Will it start? If it will, will the blade engage? If it starts and the blade engages, will the throttle work and will the mower go. Once the problem is determined you can begin repairs.
If the mower will not start, the first thing to check is the gas tank. If gas is in the tank, check the spark plug. If the plug is good check the battery. Most newer mowers have sensors in the seat that require the driver to be seated before it will start. Make sure the sensor wire is connected.
If the mower starts, but the blade will not engage, check the belts on the mower deck. Sometimes these belts will break or slip off. Putting them back on can be hard to do and will require patients or the assistance of someone who has done it before. Hiring someone to replace the belts is expensive.
If the throttle is not working, check the cable that goes from the throttle to the engine. These are just a few possible solutions. If there is a problem with the engine it will have to be fixed by someone who has experience with small engines.