You either love wrinkle paint or you put up with it hoping that a machine in shiny black comes your way. I happen to love the finish. It's very rugged, hides a myriad of metalwork sins, and can come in some very sober and serious colors. As great as I think this paint is, it is a magnet for dirt, grime, and crud. Dirt invariably make its way into the wrinkles and makes your typewriter look tired and grungy. However, the innate ruggedness of the paint makes it easy to clean. This is the process I use. Your mileage may vary.
To start with you need some simple supplies. A couple of soft cloths, a small Tupperware container, a household laundry detergent without dyes or perfume, an old toothbrush, a utility spray bottle, and a blue Olympia SM3 (or whatever you happen to have). As with the other How-To, I recommend you dust/wet-dust your typewriter first. It takes a minute and "Water is the best solvent."
This process assumes that your typewriter is clean on the inside. There are some really good and some really bad ways to clean the inside of your typewriter. I'll share some of those other methods another day. This, however, is just an exterior clean.
Everything begins with the cleaning solution. I like to use 1 part detergent to 4 parts water. However, I have been known to eyeball it. Whatever you think is right. I like to have just a hint of bubbles on the surface.
Take your toothbrush, dunk it in the cleaning solution, and start scrubbing the typewriter. Use a fairly vigorous scrub. Depending on how dirty your typewriter is the suds will slowly change. They'll range from pale white to mud brown. The pictured machine was fairly clean to start with, so the suds are pretty white. The suds on one of my Royal Aristocrats looked like a mudslide. While you're cleaning, your nose will get a nice whiff of 50 year old dirt. Somehow, when you clean using this method, the smell of the past is rekindled. It's an odd smell, but you will learn to love it.
After you marvel at the dirt hidden in the wrinkles, take the spray bottle and use it to spray down the area you just scrubbed. Catch the run-off with one of the cloths. Work in sections and you will notice a significant improvement. Repeat until you are satisfied.
As a finishing touch I like to spray some Pledge on a cloth and go over the surface. Pledge adds a little shine and happens to smell nice.
If you have fingerprints from inky fingers, you might be able to get them out. At the very least, you will make it look a little better. I know there are other methods out there (Richard Polt uses PB Blaster to great effect), but this one has no harsh chemicals so your wife won't hate you for stinking up the house with kerosene.