One way is to heat the material. If it readily oxidizes and turns bluish black, with scaling, it's carbon steel.
Stainless will generally tolerate greater heat without scaling, and turns a brownish color in the process. Of course, the alloy makes a big difference. The 300 series of stainless is non-magnetic, which is a good test for much of the stainless you'll encounter, but not all. In a work-hardened condition, even the 300 series can be mildly magnetic.
Color is also an indicator, again, depending on the alloy. The 300 series all have a yellow cast, very unlike carbon steel.
300 series is not affected by nitric acid. It is used for nitric storage and distribution.
Harold