I would look to YouTube for videos.
It's not really than complicated, though.
I first don some nitrile gloves.
Take a cleaning rod, attach a bronze brush of appropriate size and squirt it with some solvent. Hoppe's #9, CLP just to name a couple.
Open the cylinder if double action, remove if single action. Run that brush back and forth through the barrel several times. Ordinarily you would do this from the breech end, but that's kind of hard to do on a revolver. You want to be mindful of the crown (muzzle end, where the rifling stops), and I put a towel over the inside back part of the frame so's I don't accidentally smack it with the end of the brush. Don't reverse your stroke while the brush is in the bore.
Now run that brush through each chamber in the cylinder.
Then I get an old toothbrush and some Q-tips for the nooks and crannies, around the forcing cone, top strap, etc.
I wipe everything down with shop towels. At this point you would run dry patches down the bore and chambers until they come out dry. I am lazy, so I use a Bore Snake for this part of the process. Couple pulls through for each.
Then I push the ejector rod, put a small drop of oil where it slides into the cylinder, work it back and forth then wipe off the excess. Make sure there is no crud under the ejector star at this point. Couple times a year I will put a drop of oil in the guts and work the action to spread it around. Sparingly, you don't want excess dripping out.
Then the oily rag, though I am a fan of the silicone impregnated reel and gun cloths. Then another shop towel to remove the excess (you only need a thin film).
Reload, if you so choose, and put it back where it goes.
I have a felt mat with non permeable backing, but used to do it on the coffee table on top of some shop towels. Smell of the Hoppe's gave my missus a headache, so I got some CLP. Now I have a workshop so it doesn't matter.
Most, if not all of these things can be had at Academy, Wal-Mart, Bass Pro and the like. I started with a caliber specific kit from the range/store where I shot my first gun for the first time.
You'll get it down. Like I said, it's not that hard. You'll be an old hand in no time.
Hope this was helpful. Enjoy your new gun.
Well, Beretta686 simplified this while I was composing this novella.