Do NOT use a vacuum, they can, and do, build up static, which, if it is discharges through one of your components, will kill it.
The best way is to take everything, vacuum your empty case.
Then, each heatsink, clean off excess thermal paste with a soft, lint free cloth. Coffee filters work best, but toilet/kitchen paper will work well too. Do it until no more grey is coming off on your cloth. Then, vacuum your heatsink to get the worst of the dust off. Then, runs the heatsink under water to get the surface dust off, and use a hairdrier to clean, as it will blow off any excess.
Then for each component either do it by hand with your hands, tweezers and cloth, or use a can of pressurised air to blow off the dust
Just buy some compressed air cans. They are cheap and work great.
I Don't want to try doing the empty case taking everything out.. So is a hair dryer ok?
No. It is the fast moving air that makes the static. Compressed air doesn't move that quickly, but is in a concentrated area, and so it does move dust very well. You can get anti-static vacuum cleaners, but to get one just for your computer, not worth it I don't think unless you work building computers and do this sort of stuff regularly.
If you aren't taking everything out, compressed air is your best bet, but you will have to take the dust out by cloth/hand because the air blows it, not sucks it up. It is worth the taking everything out approach to clean it to "as good as new"
If you use industrial compressed air, be sure to keep one hand in contact with a unpainted part of the computer case in order to prevent static discharge damage.