If it's covered in inch thick hard grease and dirt, I use "gunk" degreaser (99¢ store has some off brand that works.)
Let that soak and scrub it off with a small wire brush (again, 99¢ store. They have some pretty soft ones in the auto section, 2 for 99)
If the aluminum is really corroded, I use the wire brush on the whole thing to get all the corrosion off.
Then it's wet sand with finer and finer grits, steel wool, and then a polishing wheel on the grinder.
That's if you want it mirror finish. If you just want it nice looking, after you get the grease and crap off, a green 3m pad and some steel wool will clean it up pretty good.