Foil won't help at all. First, remove the anodized coating. I use Extra Strength Eazy-Off. Apply to a small area, let sit for a couple of minutes then scrubb it off. I use a soft brass brush for this task. Rinse immediately and do it again (failure to rinse will cause the caustic in the Easy-Off to eat into the alloy if left on too long...


After removing the anodizing, time to polish. I use wet and dry sand paper at first (1000 to 2000 grit) after which I switch to my yard sale purchased home made polisher, coupled with two grades of polishing stick compound...


I should add that, as often as not and assuming no anodizing, the machine polisher can be used without sanding anything, offering results like this with only a few minutes of effort.

From this...


To this...