Hello niles2001,
Pick-up a can of Brasso® at the hardware store as well as plenty of cleaning rags.Ideally you should remove the kickplate for cleaning but not necessary.Be advised that once you start working with this product,you may end up cleaning stuff all day long.Good Luck!

If you buy a new kickplate, it'll stay pretty for a long time (unless you kick it a lot). New brass products have a coating on them to keep them shiny. When that's gone, you have to polish them frequently to keep up the shine. It might not be worth it to you to keep the old one polished, especially since (as Matches said) you should ideally remove it before polishing. Otherwise, you'll get the rest of the door messy and have to clean that too.

Once you use up all of your elbow grease on polishing up the kickplate, spray it with a clear exterior finish.