I assume you are referring to the front shoxs & not rear suspension ? rear suspension comes in so many different formats I'll not even venture down that route.
Basically there are two types of front shoxs, the older cheaper heaver ones have large coil springs in them where there is basically a stud that runs through the spring & then on the top of the shox is an simple adjustment normally marked with an arrow indicating + - tension, screwing down increases the spring make the compression stiffer / harder, backing it off makes it more bouncy softer (for what of a simple word) some shox have a cable from the handlebars going to top of the shox on one side this is to lock the shox for smooth road use, if you have this cable & trigger release type maybe its stuck.

The later better quality shoxs are air operated no spring much lighter normally the body is ally as well, these require a trip to the LBS to adjust.