Just like in polishing paint.... Prep is key to polishing aluminum to a mirror. Depending on the grade/ condition of aluminum you are starting with..... You would sand with a d/a sander . If the aluminum is pretty rough... Start with 220, then 320, 400, 600. You must make sure you sand out all the previous grits scratches... If you don't, you will see them when you start polishing. Then you will have to go back to sanding all over to remove those missed scratches. If done right... After 600, you will have a reflection, although a very hazy one. From there, you can keep sanding with 800, 1000, 1200. But those aren't necessary if using rouges with buffing wheels or "airways".
If using airways, you need special safety flanges to help keep the metal center that mounts to the buffer from separating and flying apart. I could walk you through what rouges and wheels to use, but they don't sell them here and don't know what the policy is. But... I must warn you... You could talk to 5 different polishers and get five different ways to polish and what products to use.
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