First, you want a .38 caliber cleaning kit and a screwdriver that fits the screws. A screwdriver set an be purchased from Brownells at:
www.brownells.com
Note that there is a small screw at the front of the sideplate. Carefully remove it and put it in a container so it doesn't get lost.
Unlatch and open the cylinder. At this point you can slide it and the yoke forward and off of the frame.
Pull the yoke forward and off of the cylinder assembly.
You can now use your cleaning rod and brush to scrub out the chambers and bore. Follow with patches and solvent, and then lightly oil.
Put some solvent on a small piece of cloth and wipe off the exterior surfaces. Pay particular attention to the back of the barrel, under the topstrap, and around the breech face, Also wipe off the exterior surfaces of the cylinder and yoke.
Cock the hammer, put 2 drops of oil down into the slot (and no more) and double-action it a few times to spread the oil.
Put a drop of oil on the yoke barrel, spread it around, and slide it back onto the cylinder.
Slide the cylinder assembly and yoke back onto the frame and replace the screw you removed.
Rub all of the exterior surfaces with a lightly oiled rag, dry any access, and you're done.
No, you don't have to remove the sideplate simply to clean the revolver.