I live with a lot of pets so early on my wife and I purchased a dog grooming kit from a pet store. I figured I might be good at it because I had a background in cattle grooming through 4-H when I was younger so why not give it a whirl. Previous experiences with grooming cattle taught me to be patient with animals, and I'd never been kicked before so I am pretty fearless.
Our dog is a mixed breed doodle and generally very calm anyway so I had good luck trimming him. We also have three cats, but only one in particular that's very fluffy and in need of an occasional hair cut. It usually goes well but sometimes he's temperamental. Over the years I've gotten better at hiding the mistakes from when they move too quick, but often there's no more than a patch or two where I cut too much off. The embarrassment in poor old fluff's face when he comes in from another trimming... He used to bite and claw a lot, but he gets so matted up it's pure relief when he gets a good buzz cut.
Cat's aren't much different to trim only they scratch way more, so it's best to wear gloves and sturdy clothes. Beware the hind legs that come out of no where and try to scar your thighs. It's better if you are careful and just go slow so the cat relaxes a little. It's not perfect advice so don't go too slow either, act fast when they are calm and you can accomplish a lot quickly. It's a power move for bellies, some cat's will dig in here, but if the mats are coming free they usually relent. Keep a cool head and watch for biting, kicking, scratching and you'll do just fine
So that sums up my level of amateur expertise, I tend to look to the experts for real tips. Here's some tips I nabbed from the Internets (thanks My Pet & I blog - top search result presented on google)
Seven tips for grooming your dog at home:
Regularly brush your dog's coat to prevent matting.
Trim your dog's hair – but use caution.
Safely trim your dog's nails.
Check your dog's skin as you groom.
Teach your dog to enjoy grooming sessions.
Regularly check your dog's ears.
Don't bathe your dog too often.
All good tips, except I usually forget to do the first one as often as we should. Live and learn, until next time, keep it fashionable!