I believe that my PS3 is full of dust and therefore the fan goes on max as soon as I start a game.
How can I get rid of the dust inside on the heat sinks and fans without destroying something?
The above suggestions are good (essentially), but for me they were by far not enough. I have a preordered original 60gb Fat and it was running like a lawnmower for months. I tried everything, but it just didn't help me.
That was until I tore it apart and hand-cleaned every last dusty part of it. This is not for the faint of heart -- you would do well to have some experience handling computers first. For example, take apart and put back together your laptop (desktop pcs are too easy). And for me the first blue screw was completely stripped so I had to use pliers to get the damn thing off.
But I did this four months ago, and it ran on the lowest fan speed + fan speed number one the whole time. Recently I noticed it starting to move up to fan speed one a little faster than before... the dust is coming back... but this is of course only a temporary setback. There will be nobody to stop us this time.
Guide: link (You don't mention what model PS3 you have, but there are teardown guides for all of them. Google is your friend.)
Buy a can of compressed air(in a lot of places you have to be 18, so possibly have your parents/whoever) and unplug the PS3. Spray the compressed air through all the vents and such. wait about 5 minutes to be safe( let all the liquid stuff dry that can come out as well as possible condensation) and then see if that helps.
There are some good dust discussions above, also be aware of pet hair. If you don't have pets, ignore this, but if you do have pets try getting the ps3 off the ground and into a cubby, compartment, enclosed space, etc... to get it away from the destructive substance that is pet hair. I just heard a story on NPR about how bad pet hair is for the efficiency of electronics, especially computers and video game systems.
I keep my PS3 in a compartment about three feet off the ground with a door. I have two long/short haired cats and although pet hair still finds it's way up there, it would be significantly worse if the ps3 was on the floor.
Open the case, then use one of those air-cans that one uses to clean a PC. It's very soft, so it should be fine to clean out the dust.
Buy a small hoover that can be reversed to blow out air. Blow is MUCH better than suck. Then you can also blow away dirt from those hard to reach places in side doorways and sliding doors. They are powerful enough to blow leaves too. On electronics give it a quick blast of no more than 3 or 4 seconds as you want to avoid static building up especially as I presume the PS3 has no proper earthing with a 2 pin adapter at the back going into a 3 pin UK plug.
The main source of noise from a PS3 is the optical disk drive. One can not do much. Placing the PS3 flat is better than on its side.
I tried sucking all the dirt and dust around the edges of my ps3 and it worked just fine doing that so do that