Research is where the trail begins for finding relics. You can bury your nose in books, maps, or many other ways. I guess the biggest help you could do is just find somebody else that's "into it" and ask them for help. A lot of people recommend joining a local club but sometimes there aren't any local clubs to join. But most people know somebody that is "into it" or had formally been. So finding that kind of person can be a big help for starters.
Other wise you're gonna have to wade through a lot of junk to get to what you're looking for. A good local history book will get you in a decent starting place. You can learn the who's and what's, and a ball park of the where's. Finding the where's is the hard part. I'm about to give up a big secret here but here goes.
If you are wanting to look for Civil War relics, the maps they had in the 1860s are very vague and our modern maps only show modern roads. Granted, some of the roads we have now travel similar routes to those back then but "similar" could me the difference between being a half a mile or more off from the spot you're looking for. So that said...in the late 1880s and early 1890s, the government done a topo survey of Tennessee. They had engineers draw up very very accurate maps. Find those maps (usually you can find one at the library) and make a copy of them. What this does for you is this...it shows you the roads in relation to topo features. The roads in 1880 would have been there in 1860s for the most part. So you can know where they crossed creeks and rivers, and all that important stuff. Then you get the modern maps out and overlay that info.
Sometimes you get lucky and the likely areas aren't modernly developed. More often than not in today's times, you'll find that the old camp site is now part of a parking lot, or shopping center.