First of all, a great way to keep your skates clean for competitions is to wear boot covers. They are pretty cheap and you can buy them at just about anywhere they sell sporting goods or figure skating supplies. They come in a variety of colors and sizes.
A good way to keep the heel of your skate clean is to put hockey tape around it. The tape also protects the heel and base from getting ruined if you do a lot of lunges.
If your skates are already dirty or looking a bit dingy, you could try nail polish remover on them. Just put some on a cloth and rub it over scuffed up areas on the boot. This will remove some of the dirt, but not all. It's just a quick and easy way to relatively clean skates.
If you have a competition or other important event, I would suggest painting and polishing your skates if they are dirty. Judges HATE dirty skates and laces! You can either buy skate polish or paint at a sports store, or you can get them professionally done. Make sure if you are doing the painting yourself that you clean the skates prior to painting. It will help the paint stick easier and you will have less clumps or built-up areas. I usually prefer to trust my skates to the professionals because I tend to do a very messy job! When you do paint your skates, make sure you take out the laces and do one side at a time letting each dry in between. Don't forget to do the tongue! It also helps if you but some tape around the base of your skate so that you don't get paint on that area. After you paint and let dry for about 24 hrs., give your skates a nice finish by rubbing in a circular motion over the entire skate with a shammy or old rag.