Yes, you can groom your cat by yourself but how should I go about it?
First, you need a really good clipper, do not buy cheap ones because it does not work. A clipper under $40 is not worth it. I bought this Andis 22360 AGC Super 2-Speed Professional Animal Clipper with Locking Blade and it was $130+...now I see it came down to $125.
If you buy Andis 22360 clipper it comes with Andis CeramicEdge Blade 10 . #10 brade is very good size for cats. It is good idea to buy another set of brade because you need to replace it soon or later. My brade rusted about using 6 months...just because I didn't oil it and clean it property... for a brade to last long time, you need Clipper Oil.
The clipper gets really hot real quick easily but your cats won't have enough patience to wait until the brade cools down everytime it gets hot! In order to continue grooming you will need a Cooling spray. It cools the brade in seconds and you can continue your grooming!