The first thing is to note whether your part has has been anodised or not.
It looks like the brakes in the first post has only been cleaned, the anodising hasn't been removed. Without removing the anodising, all you can do is get the finish near its original condition, which might be a satin type of finish. Use a solvent to clean off the dirt, and then use a metal polish like Autosol which is a mild abrasive.
Autosol won't remove anodising, you can with abrasive paper but it will take a long time and a lot of effort if done by hand.
To get the chrome-like mirror finish you need to have an unanodised part (eg Campag N Rec hubs) or you need to remove the anodising (eg the stem in the pic up-thread).