First, be smart from the very beginning. Pulverize all teeth, burn off fingerprints, and disfigure the face. Forcing a DNA test to establish identity (if it ever comes to that) might introduce the legal/forensic hurdle that saves your ass down the line. An unidentifiable body can, in a pinch, be dressed in thrift store clothes and dropped in a bad part of town where the police are less likely to question it. I don't reommend that disposal method, I'm just saying an easily identifiable body is an even bigger threat than the opposite.
Assuming you have it inside a house where you can work on it a bit, the first thing you want to do is drain it of fluids. This will make it easier to cut up, and slow decomposition a little bit. The best way to do this quick and dirty is to perforate the body with a pointed knife, and then perform CPR on it. Cut the fronts of the thighs deep, diagonally, to slit the femoral arteries. Then pump the chest. The valves in the heart will still work when dead, and the springback of the ribcage can put apply a fair amount of suction to the artria. Do this in a tub. Plug the drain, and mingle lots of bleach with the bodily fluids before unplugging the drain to empty the tub. This should help control the stench of death, which would otherwise reek from your gutter gratings. Do everything you can to control odors. Plug in an ionizer, burn candles, leave bowls of baking soda everywhere. Ventilate the room in the middle of the night, but otherwise keep it closed. Keep the body under a plastic sheet while it's in the tub.
If you want to bury, I recommend seperating the body into several parts, and burying them seperately. For one thing, it's easier to dig a deep enough hole for a head than for an entire body. this reduces your chances of being discovered while you are actually outside and digging the grave.
That is the one thing you can't do inside the doors of your house, and represents a vulnerable moment you want to keep brief, under 2 hours. Do it between 3 and 5 am. It's also less likely for someone to call the police if their dog digs up some chunk of meat, than if they dig up an enitre body. They may assume it's an animal carcass disfigured by decomposition, and leave it alone or dispose of it. It's also more likely that the dog will consume all of it before anyone knows the difference. A whole skeleton is another story. You can cut a body into 6 pieces faster than you think. It's not much different than boning a chicken, but it takes more work, a big knife, and time. A hammer will be useful for pulverizing joints or driving the knife deep where it doesn't want to go. Anyway it's wise to crush as much of the skeleton as you can along the way. It will aid in making the body less identifiable for what it is as it decomposes.
Don't return to the same site 6 times for 6 burials.You'll attract suspicion from anyone nearby, and you'll wind up placing the body parts close enough together to be found by any serious investigation. Put them in plastic bags with lots of bleach, and store in a freezer until you have enough time to bury them all.
Depending on what tools you have available, you may find that you're get really good at deconstructing the body. You might prefer to slowly sprinkle it down a drain without leaving your house. This avoids the long-term risk of discovery associated with burial, and the overwhelming supply of bacteria in a sewer accellerates deconomposition, whil e providing a convenient cover smell.
Truly grinding down a body takes a lot more work, and you run the risk of fouling your plumbing and calling in a plumber. So don't try it unless you know how to clear bones and meat out of a drainpipe. A good food processor can be useful. But don't over-use it, or power drills or saws. They're noisy and they attract attention. And forget the kitchen sink. It's better if you actually remove one of the toilets in your house from its base, which will give you direct access to one of the largest sewer pipes that enters your house. Follow any disposals with lots of bleach and then run the water for 5 or 10 minutes on top of that. And plug that pipe when you're not using it, to prevent any sewer gasses from backing up into your house. Usually, a U-trap inside the toilet does that for you.