If your computer has ever just shut down only to miraculously recover and work just fine later, it may be overheating due to too much dust hindering the fan or blocking the vents. If you're lucky, the fan will start making noises before it reaches a sufficient state of inefficiency that your computer shuts off due to overheating. The sound of a fan struggling to cool a CPU despite a clog of fine dust is one I've grown to recognize pretty well and I'd been hearing it a lot lately from my husband's laptop over the past month. I told him I'd have to go in for some minor surgery and clean it up or he'd start experiencing shut-downs (or could damage the computers delicate parts).
You can pick up canned air in any electronics shop or order it from Amazon Japan for about 500 yen a can.
Unfortunately, we didn't have the requisite surgical equipment on hand as I'd used up all our canned air last time I cleaned out a computer. In Japan, cans of air are often called "air duster" (エアダスター). The one we got was called "dust blower" but they're really all the same thing. If you've never used one of these, the can gets very cold when you shake it and the air sometimes comes out with frost if you get too close to the target with the nozzle.
The first step in dealing with my husband's laptop when its fan starts to cough and wheeze in the dust bowl it's currently residing in is to remove the back. This is not all that hard if the screws aren't too tight and, thankfully, last time I put the backing plate on I didn't over-tighten them. Sometimes you have to use special small screwdrivers. Fortunately, a set of them can be purchased at 100 yen shops in Japan. Unfortunately, most of the sets have really bad handles that are hard to get a grip on. If your screws are really tight, you'll need to invest in better tools.
Once the back is off, you should touch something metal to make sure you don't have any static charge (or you should be wearing an anti-static wristband, but I personally don't have one). This should stop you from accidentally frying any neighboring components with static. I also have to remove a covering plate from the fan. The cover has Lilliputian screws which I tend to drop into the the cavity next to it, especially when I'm trying to put the cover back on. This is about the time that I wish my cheap 100-yen-shop-tool set had magnetized heads.
Once I get the fan revealed, I blow the dust out into the sink using the canned air and some fairly good balancing skills (lest I drop the machine into the sink). Unfortunately, the canned air was so cold that it left frost around the edges and I had to wait for it to thaw and dry out before doing more. I guess I must have blasted too close to the machine. Once the air had done all it could, I took a Q-tip to the fan. Careful and gentle swabbing showed it was pretty dirty between the blades.
Even more unfortunately, so much dust had caked up in the vents that the air alone could not dislodge it. I had to go in with a toothpick and try to loosen it up and dig it out then re-blast with the air again to clear it again. That might seem like a little dust to us but it's quite a big glob for a laptop computer which has tiny little vents.
Once I was satisfied with the fan, I removed the plate over the RAM modules and CPU (which have a ventilation grill over them). I blew out the dust around them and inside the heat sink though those were not nearly as dusty. I also decided to give the rest of my husband's laptop a good clean as he's not very interested in how it looks and often lets it get pretty cruddy.
Sparkling clean but marks on the display can't be cleaned off. Fortunately, the marks can't be seen when the computer is in use.
The hard part about cleaning laptops is dealing with the screen because you can do a lot to screw it up if you use the wrong fluid or even leave water on it. Usually, I use a special lint-free cloth designed for computer screens. I dampen it with warm water and wipe off the dust. I then dry it off and buff out any dried water marks using the sort of non-abrasive, ultra-soft cloth designed for camera lenses. In the case of my husband's dusty machine, I also cleaned the entire case. I can't exactly say it looks like new because he's scratched up the case pretty well from tossing it into his backpack and the screen has picked up some imprinting from the keyboard but it certainly looks better and the fan is breathing freely again.