Only real brass will polish to a bright, shiny finish. One way to check for real brass is to use a magnet. Brass is non-magnetic so it will not attract a magnet.
Many people use natural, homemade polishers but the few I have tried did not work. I wish I had a way that didn't use such harsh products, but I haven't yet.
This is what I use to polish brass.
Gel or liquid stripper
Brasso or other metal polish
Tough paper towels
Toothbrush or other soft brush
Small wire brush
Citristrip is my favorite stripper but it doesn't seem to work as well on metal pieces. I tried to use it first and it didn't get the old, dirty clear coat off so I used a stripper that is stronger.
Be sure you are in a well ventilated room or outside for this project. Both the stripper and Brasso have a strong chemical odor.
Strip the piece. While wearing chemical gloves and glasses, pour and brush stripper all over the piece then let it sit. Read the directions for your stripper for recommended time. My stripper only needed 15 minutes. Use the toothbrush or wire brush to scrub off the old clear coat and dirt. Wash off all the stripper and dry with a paper towel. Also, rinse off your toothbrush and wire brush.
You might already notice a difference in color!
Shake your Brasso before use. Pour some directly onto the piece or onto the toothbrush. Scrub the piece with the toothbrush being sure you get every crease and hard to reach spots. You will notice that the Brasso will start to turn green or look dirty. Add more Brasso as needed.
You will notice a color change almost immediately when you start scrubbing.
Once the entire piece is scrubbed, rinse with water and dry off.
Rinse the piece and wipe clean and dry with a paper towel.
Over time the brass will tarnish again. I leave mine natural and will polish again as needed but you can seal it with a clear coat.