Almost any lamp can be polished back to their original glory with some elbow grease and time. Brasso (which Flipturn already mentioned) is a great product for brass , and also some automotive polishes are capable cleaning that up (for instance, Duragloss liquid metal polish is one I have used).
A dremel tool with some different wheels will speed up the process but patience is your friend.
Thanking you so much for your response. I will try this.
Is it real brass? I tried to polish real brass once and my arm almost fell off with no improvement because I didn't realize that it was lacquered.
If it is brass and look like real brass chances are they have a lacquer on it. The reason I say this is that brass will tarnish fairly quickly and can turn black. What keeps the brass from tarnishing so fast(and keeps it shiny and gold-ish) is the lacquer which keeps the air from tarnishing. Eventually (takes years), that brass shine will tarnish even underneath the lacquer though. The way to deal with that is stripping the lacquer... then shine up with a brass cleaner once that lacquer is off, and then re-lacquer. Sometimes something will look like it is solid brass but is actually brass plated. I think you could still try the above method though, and you will eventually figure out what metal is all the way through. In either case, you could try shining it up with a brass cleaner, if nothing happens to make them look better, you will need to strip it. That means there is lacquer that needs to be stripped to get to the brass. Then try to brass cleaner it again. (TRY BRASSO cleaner) If still nothing looks better, then the metal is probably a cheap metal that has been painted to look like brass and can just be repainted and finished off with another lacquer or polycrilic finisher. I hope this makes sense.