Unlike cleaning cast iron, there is no easy way to clean aluminum other than elbow grease. I have been able to remove baked on crud by placing pieces in a self cleaning oven and then cleaning the oven with the oven settings for that process.
Restoration of scraches or other light damage, requires a lot of patience, sand paper, steel wool and Mother's polishing cream. Use the finest sand paper or emery cloth that will get the job done and move to the next finest and keep going with the elbow grease and sweat labor. Finish with Mother's polishing cream (available at WalMart or any automotive store). I've also been told that a coat of wax after you have finished polishing will aid in preventing the oxidation that occur over time with aluminum pieces.
WAGS Member Jake Weber has created an illustrated tutorial on polishing aluminum.You can see it here: Polishing Aluminum
METHODS REPORTED BY OTHERS (UNTRIED BY THE WEBMASTER OF THIS SITE)
To remove stains and discoloration from aluminum cookware, fill cookware with hot water and add 2 tablespoons cream of tartar to each quart of water. Bring solution to a boil and simmer ten minutes. Wash as usual and dry.
I also boiled a mix in a deep pan and set my aluminum pieces in for up to 20 minutes. It worked beautifully without damaging the patina as oven cleaners might do. Cream of Tartar is available in grocery stores in the spice or cooking deparments. Remember, cream of tartar is an acid so I would suggest experimenting on the dilute side of thier equation.
Another method reported by Steve Stephens.
At the recent Griswold club meeting there was a Griswold aluminum 280 cornstick pan that looked brand new. The owner had had it blasted with walnut shells leaving a beautiful, shiny satin surface. He said that the pan was terrible looking before being restored. I really thought it was an unused pan when I saw it. The walnut shells are not abrasive as sand would be and softer than glass beads which would move the metal around.