I am looking to rent a basement. My purpose is to store documents and clothes, for several years. Hence I need to be sure that this basement is dry, that my documents and clothes won’t be damaged over time. I find it hard to see that when visiting the basement. How can I tell ?
A humidity measurement is the first line of defense. The relative humidity should be appropriate for the local climate, say 40-50%. If it's higher, find out whether a dehumidifier can be used (with a floor drain, ideally).
If you have an unfinished section of floor, duct tape a square of poly sheeting for a few days and see how much moisture accumulates. This doesn't give you an absolute answer, but it tells you how hard you'll have to work to keep the air humidity down.
Otherwise, look for visual cues. Dark concrete. Staining. Mildew. Of course, you could also ask the owner.