ok, here's what you need to do. If the scratches seem to be like a haze, you may be able to get away without using polish and skip right to the glaze. This process will take some time (set aside a nice Saturday) but it will basically fully restore your car's finish. There's no easy way to get the final results like using only one "cleaner wax" compound or some other magical solvent. There are steps that need to be taken to do this right. A detailing shop will do these same steps except charge you a butt-load of money. I do this to my dad's cars and I successfully de-keyed my older sister's car (which is a feat considering she left it there for over half a year and never washes her car)
First, strip the wax off the car. Use something like dishwashing detergent or even better an actual wax stripper. Then thoroughly hand wash your car. Really scrub it and get all the junk and minute particles off of it. This is very important because if you don’t do this within the next couple steps you can actually introduce more scratches into your finish.
Once the car is stripped of wax and cleaned, (I suggest you rinse with some distilled water or filtered or something [mr. clean thingy without using the soap, just use the filter portion of it] that way no minerals get stuck onto the car.) You need to let the car cool as waxing it when the metal is warm to the touch wont be as effective. Depending on the severity of the scratches, you need to either polish, or glaze your car. Polish is made to, well, Grind off "layers" of paint to even out the surface to make the scratches disappear. Polish will produce a very hazy finish but sets the groundwork for the next step, glazing. I suggest you go ahead and give your car a nice polish anyways. Clean the polish off with moist towels you don’t care about (or paper towels without ink on them) and then make sure the surface is relatively dry.
Glazing. You need a fresh application pad for this. Glaze is the equivalent to high grit sandpaper as opposed to the polish, being the low grit sandpaper. This produces that mirror surface that seems to be underneath a clear coat of wax that makes the car so incredible. Apply same way you would polish. This step is amazing. It flattens out the surface of the paint and makes it very smooth. If you ran your fingers over a glazed surface vs. a non-glazed surface, you can easily tell the difference. (Don't do that you don't want the oils on your hands on your car at this point)
After glazing, here comes the last step. Waxing. I strongly suggest you use a canubra wax of the highest purity available. Wax on, Wax off... and now enjoy your beautiful new car.
Here's an article that says basically the same thing I did, it features some different lesser known brands of polishes glazes and waxes but the meguires 3 step system works just fine. Car detailing tutorial