Dand
I am not a gun smith, but have worked on a S&W or two. I would get a PROPER fitting screw driver, lay the gun down on a clean white towel, and take off the grips. then remove the screw farthest forward on the frame, under the cylinder. Now open (swing out) the cylinder, and slide it forward. It should remove from the gun. Remove the other two frame screws, then gently tap around the frame (not on the side plate) with a rubber or leather mallet. The idea is to work the side plate up and off the gun. Do not try to pry it, as it is closely fitted, and will cause an unsightly burr to the metal. Once the side plate is off, take a close look at the inner workings, checking for dirt or other assorted garbage.
Now, how far you want to go in dis-assembly is up to you, but it is fairly straight forward. If you don't feel comfortable doing so, I would get an aerosol can of "crud blaster", or something similar, that leaves no residue, and give it a good washing out, including behind the thumb latch. When it is dry, lube with a light gun oil, re-assemble, and try it out. Finding a dis-assembly video is a good idea, by the way, or an on line schematic. Worst case - A trip to the gunsmith anyway. Good luck...
Larry