Before. Your clippers will dull lots faster if you clip a dirty dog. When I do Zoey I give her her bath, then clip, and then I rinse her off in the tub with just water afterwards because I always seem to leave little pieces of hair all over her.. :-/
I might add that if you are going to be bathing before you clip, ALWAYS brush the dog thoroughly BEFORE the bath, to remove all tangles and matting.
You should be able to run a comb through the dog's coat, all the way down to the skin, before bathing him.
If you cannot get a comb through the coat, you have not brushed him out well enough.
If you do not remove all matting and tangles before the bath, bathing will just tighten the mats and make them more difficult to remove.
Personally, if I'm going to be taking a lot of length off the coat, I will sometimes pre-clip before bathing.
If you are going to be giving your dog a shave-down (by shave down, I mean leaving a half an inch or less of hair), and he has a lot of coat that's going to be removed anyway, it saves drying time and shampoo, if you use a cut down blade to remove the majority of the hair BEFORE the bath.
Then, after he's dry, you can use a finishing blade to make the haircut look smooth and uniform.
I worked under a groomer for a while, and she always clipped and shaved before bathing. This way if she nicked a skin tag, more, or discovered worms/fleas/etc, she would know BEFORE she put the dog in the tub. All the trimming was done post-bath, though.
the best and only way (just for me of course), is to always bathe first, for many reasons. first, clipping dirty dogs, matts, and all other crud really destroys your tools. not only your clippers, but everything from your scissors to you brushes. What i do is go through the dog first. i only brush out/clip what absolutly needs it, which is usually not much. huge matts behind golden ears for example get shaved. matts in toes get shaved. that sort of thing. i have learned a lot through the years of grooming. i know that time is cut in half if you bath the dog, demat while you dry, then slip. its not completely true that bathing matts constricts them and makes them worse. that does happen if you dont know there are matts and dont do anything to get them out. after i shampoo, i work in conditioner into every matt. then when i blow dry, i keep a comb handy and just gently pick through the matts. the conditioner helps break them up, and the dryer blows them away from the skin and breaks them up as well. brushing a dry dog is much more likely to lead to brush burn and skin irritation than brushing a wet dog.
but general rule, most good groomers do very little pre clipping. they know the benefits to clipping clean hair, and know how much it saves time.
I do nails and straight to the tub on 90% of the dogs I do. I only pre-clip on overgrown thick haired dogs, and I do pre-brush on dogs with a lot of undercoat. I don't comb the dog pre-bath or completely demat. I sometimes leave knots and mats in because while I am fluff drying it is actually easier for me to de-mat since the stand drier seperates the hair so nicely right down to the skin while I use my slicker brush to straighten and de-mat the coat. Larger thicker matts I do work on before the bath, and use a conditioner to work the mat in the tub. I find the high vilocity drier helps A LOT with separating mats. I never use my scissors before a bath.
In grooming school we were taught to groom exactly like how pit-bull-lady does it. And that's how I did it for a long time. But I save so much more time not preclipping and just working on a clean dog. Not that I'm a fast groomer at all, I can only groom 5 dogs a day. I also find shaving pads of feet and dematting is so much easier on a clean and conditioned coat.
I groom very simarlly to Purplex in the above post and I find it gets a better finish and easier on my tools AND ME.
Dogs with long silky hair like Malteses and yorkies to name a few when they are wet, DONT DONT DONT wash there coats like you would a short hair dog. You know your hands all over the coat scrubbing in all directions. If you do that to a long coated breed like the 2 I mentioned its going to be a nightmare to untangle it afterwards. This is a tip I learned from a tv show or something. when bathing long coated breeds, put the shampoo in your hands and run it down the length of the dog's coat kinda like ironing but with your hands or you can buy a brush that holds shampoo inside it and brush the dog with the shampoo brush.
One more thing....Like Pit_Bull_ ALWAYS Brush the dog Thouroughly before the bath.
Depends.. If the dog is horribly matted, shave then bathe. If not. I suggest bathe then shave. It will help extend the life of your blade, plus if you shave then bathe, you will just have to shave again afterward to make the dog even.