You didn't specify whether your attic has flooring or just ceiling joists, or whether it has insulation. I recently removed all the sawdust & tarpaper insulation from my attic (ceiling joists only, no flooring), vacuumed out all the dust, air sealed all the cracks and openings, and am re-insulating with more and fire-resistant insulation. A few quick suggestions...
If you only have joists, no flooring, get a few pieces of plywood about 2ft wide, 4-6ft long, and at least 1/2" thick to walk, sit, and work on. Use sturdy work shoes with stiff soles to give you firm footing and help keep your balance. Move slow and steady; stomping, banging around, or dropping boxes can cause cracks in the ceiling below.
Set up a few fans to direct air across the attic and out. You will stir up airborn dust; you want to blow it away from you, not circulate it around in the attic.
Make sure you have plenty of lighting. I'm partial to 4ft long led or fluorescent shop lights. Incandescent lights make the already warm attic even hotter and can burn you if you bump into them. A clamp or two also help in confined spaces.
Wear a cartridge respirator with P95 (particulate) filters. A simple paper dust mask is better than nothing, but not much. It's well worth the $20 to buy a respirator. Goggles, not just safety glasses, can also help if your eyes are particularly sensitive. Wear gloves, long sleeves, and long pants; old rusty nails, dead bugs, rodent droppings, and years of mold and dust mites are not your friends. Use hearing protection when you're vacuuming.
You can use a mister bottle or garden sprayer to help keep the dust down but slow, deliberate movements will be less time & trouble. Any water you add will also make the air more humid (I wouldn't want that in a hot attic in the summer).
Pick up the solid debris first and seal it in heavy trash bags or boxes that can be moved without squeezing too much air and dust out of them. Keep your bags and boxes as close as possible so you don't have to carry the dirt and debris any farther than necessary. Vacuum after you've picked up anything bigger than the vacuum can handle (don't be surprised if you find more as you go).
If you use a shop vac, get drywall dust bags that go inside the vac to collect the dust. They're made to collect flour-fine dust. You'll need to change them often but they really help if you have the vac close to you. If you can, put the vac outside or direct the exhaust outside.
If you have large quantities of dust and insulation to remove get a good sized (1 - 2hp) dust collector and use 4" diameter hose to carry the dust to a bag outside the attic. I used a 1hp fan from Harbor Freight, 4" rigid PVC, and 4" corrugated drain pipe, duct-taped together. My collection bags were old sheets and cotton broadcloth stitched together into bags about 3ft wide and 6-8ft long. My setup was fine for a one-time job. Commercial operations use up to 20hp fans, 20" dia hoses, and 25ft long 4ft dia bags. With bags outside the attic, it's good to have a helper to shake them down and change them as needed.
After all the cleaning, spray foam and caulk any wiring or plumbing penetrations, any gaps on top of the walls (don't plug your soffit vents! ), and gaps around chimneys or vent fans. If you want to do even better, turn on all the lights downstairs, turn off the lights in the attic, and seal any light leaks. This can help your heating and cooling bills all year long.