Functionality is more important than looking good when the floor of your garage is concerned. Think about what fluids could possibly be leaking out of your car--gasoline, oil, antifreeze, power steering fluid, brake fluid and air conditioning freon. Not to mention any salt, road dirt and tire marks that the car drags in. Therefore, a quality garage floor cover will not only allow these elements to damage the floor, they can also make things easier to clean up.
Most garage floors are made from cement, so the most common method is painting the floor, with a paint designed for it. Moving up the scale (quality and price) is another similar product, an epoxy-based covering which has a sealant built in; it has proven to be extremely popular. Then there are mats, usually rubber, which are available in many price points, with the more sturdy models priced higher. A lesser-used, but better-looking method is to use specialized garage floor tiles.
Carefully plan out your time frame, budget and make allowances for factors out of your control (weather, keeping children and/or animals off the floor and alternate parking plans, just to name three). This is not a small task, and should be treated as seriously as any major home repair project.
No matter which route you go, all of this takes time (and of course, money). Before doing anything, consider the inconvenience factors that surround this project--time spent cleaning out the garage, allowing cleaned surfaces to completely dry, patching and allowing the patches to dry, and applying the sealant and letting it dry. Also factor in the possibility that the sealant might have fumes, and require you to keep the garage open for several days while the work is in progress.
Unless you decide on the easiest (and least expensive) method, which is painting the floor, it's a good idea to assess how much work your garage project will entail. Repairing the damage in the floors means filling the cracks, allowing it to dry and sanding (or smoothing it out) before applying the epoxy sealant. It is a bigger job than it looks, and not one from which you can quickly extract yourself.