Roskoe

You need to pull the striker assemblies out of the bolts and check for rust on the inside. You will probably want to detail strip them - most gunsmiths can do this for a minimal fee. It's a little dangerous to do yourself without a special tool made for this purpose.

Clean that area very thoroughly and lightly oil with Break Free or Rem Oil. Pay particular attention to the spring and firing pin. Use a brass brush on the inside of the bolt, and then spray with Gun Scrubber. Other than those sort of issues, the whole deal is pretty much cosmetic. Remingtons have a two piece bolt - if you look real close, the head is silver soldered in the body - as well as the handle. Put a small amount of grease on the back of the locking lugs when you are done cleaning the outside - light oil elsewhere. You will be good to go.