Very carefully. The mechanism is actually fairly simple but use caution. get gunsmith screwdrivers. Automotive or household screwdrivers will muck up the screw heads. I work at a bench with an inverted plastic box lid under the gun to catch any dropped parts.
Remove the grips and set aside. Remove the sideplate screws and set in a cup. Note which screw goes in which hole. There may be springs or small parts under the screws so be careful. The forward screw retains the cylinder crane. With it out, you can open the cylinder and slide it forward off the frame. Clean the crane assembly thoroughly, but do not attempt to remove the cylinder from the crane. You can bugger this up very badly. (Voice of experience speaking here.) Just slide the cylinder back and forth on the pin and clean under it.
Tap the grip frame with the screwdriver handle to loosen sideplate. Under no circumstances pry on it or under it in any way. Just tap the frame with the handle until it pops off. (This assumes the handle is wood or hard plastic.) Examine the works. At this point decide if you feel confident in taking it down. It's not all that complicated, but if it looks to be too much then just wipe it out with a cloth and reassemble.
If you take it down all the way note how the parts work together. I would get a manual or parts book with an exploded view for reference. I would not remove the trigger return spring. No real need to and it can cause trouble. Just leave it and the trigger in the frame.
Use caution when putting the sideplate back on. Do not force it. Press it in evenly as far as you can with your fingers and then tighten it with the screws going from one to the next and turning one or two turns at a time so it goes on evenly.
I completely disassemble revolvers after 25 shootings or 10 years, whichever comes first. Otherwise, clean the chambers and the barrel only.