If this is the kind of stopper that is pushed down on to open and close it, it should unscrew from the drain. Usually is a threaded stud on the bottom that screws into a X-shaped part lower down in the drain that has a threaded hole in it. It may be seized up with corrosion and mineral deposits.
If the problem is just a big hair clog, the big box home improvement stores sell a drain clearing gadget that is a long narrow strip of yellow plastic with a pull ring at the top and a series of sharp 'hooks' that will grab the clog as you thread this gizmo down the drain and then pull it out carefully. Usually in the plumbing repair department with the stuff for sinks.
I used one on some hair monster clogs caused by DW and Daughter, and it cleared them right out without disassembling the sink or drain plumbing.
Rich, KE4GNK/AE, Overkill Engineering Dept.
'The Silver HamShack' ('07 International 22FB CCD 75th Anniversary)
Multiple Yaesu Ham Radios inside and many antennae sprouting from roof, ProPride hitch, Prodigy P2 controller.
2012 shortbed CrewMax 4x4 Toyota Tacoma TV with more antennae on it.