Unfortunately, the one specification for you rim that you didn't post is the one needed to answer your question: the Bead Seat Diameter (BSD) of the rim. This has to match between tire and rim.

The term "26-inch tire" has been used to refer to tires fitting six different rim sizes (BSDs). They are NOT mutually interchangeable.

I assume you have tires currently mounted on your rims. If those tires are of recent manufacture, as others have stated above they'll also have the ETRTO/ISO tire size specified somewhere on the tire itself. This will be of the form "## - ###", where # is a number.

The first two numbers are the width of the tire in mm and are, to an extent, not particularly critical (there's some "wiggle room" in what size works on what width rim). However, the second group of 3 numbers is a absolutely critical; those are the BSD in mm. If those don't match your existing tires (and hence the rim), the tire in question isn't the correct BSD and won't fit.

The advice given above to read the late Sheldon Brown's article (linked early in this thread) on tire sizing is good. IMO you should take the 20 minutes or so needed to read it thoroughly.