50 year restoration project
I just finished a project involving digitizing and restoring analog tapes going back to 1962, covering the full career of a name-brand singer - sorry, no names. When I signed on, I expected I was going to have a bunch of professionally recorded tapes. WHat I got included some of those, but also included a lot of "Throw the cassette player on the front of the stage" type recordings. I had every kind of problem you can imagine, from tapes recorded at way too low a volume, to seriously overloaded and clipped tapes to tapes damaged after the fact by strong magnetic fields. I even had two with constantly changing azimuth, caused by a serious build-up of tape residue on the capstan wheel, which makes the tape ride up and down enough to override the guides.I don't know what your software budget is like, or whether you can justify the expense, but I'll offer the following. I started out using a lot of different plug-ins, including a bunch from Waves, Voxengo, Cakewalk, etc. By about halfway through the project, and through to the end, I was using just two. Izotope's RX2 Advanced and Ozone 4.
The procedure of getting a noise profile and removing the noise, being careful not to remove program material, has been described by prior posters. But with RX2, you can do that, then go in and remove individual sounds, like a tapping foot on the stage, or an audience cell phone. And the Declipper function flat-out amazes me every time I use it. You can take a badly clipped digital recording that a couple if years ago would have been destined for the trash, and turn it into a usable recording. Astounding! Ozone is a mastering plug-in, and I'm not a mastering engineer, but even in my hands it does a creditable job restoring the sparkle to old, muddy recordings. It's not going to create something that isn't there, but if it has a thread of something you want still present, Ozone will bring it out.
Disclaimer: I don't work for Izotope, and I don't receive any financial remuneration from them for recommending their products, although they gave me a free t-shirt once.