For a basic cleaning, you'll need:
-A can of automotive disc brake cleaner (an aerosol degreaser)
-A powder/copper/lead solvent (for convenience, usually an all-in-one product)
-A .40 caliber bore brush and rod
-A can of gun oil (I like Rem Oil, it's cheap)
-Clean patches and rags
-An old toothbrush
-A quality flat-ground screwdriver
Start by unloading your gun. Remove the forward-most screw and slide the cylinder off the frame (this is not necessary but it makes cleaning a lot easier). Now, push a patch with the solvent through each chamber, then scrub the crud out with the .40 caliber brush. Wipe powder residue from the front of the cylinder with solvent-coated rag. Push the ejector rod back and spray underneath the star with the brake cleaner. Scrub out any stubborn gunk with the toothbrush and then wipe it clean. Spray out the chambers with brake cleaner, then run a clean patch through each of them. While the cylinder is out, take a rag with solvent and the toothbrush and scrub away crud from the area where the barrel meets the front of the cylinder. Wipe off the recoil shield at the back of the frame (don't let any solvent drip down into the internals of the gun!). Clean the barrel, if needed, and reassemble. Wipe down external surfaces with a lightly oiled rag, and put a drop of oil on the ejector rod. Check for function and you're done. It all sounds more complicated than it really is.
Depending on the tolerances of your gun, it will take a pretty significant amount of environmental crud or firing residue to clog up your gun. Preventative maintenance like this will assure that buildup is easily removed, as it will often wipe off with little effort if done right after shooting, rather than if left unchecked for thousands of rounds. I would take the sideplate off after 3,000 rounds or so to clean and oil the internals.