If all you want to do is get rid of the dust in it, I would simply recommend blowing compressed air through the vent holes.
There could be issues with heat due to little, or bad thermal paste, this will show you how to get to it.
The tools you'll need are a No.2 Phillips, and perhaps a No.1.
Something narrow with a sharp point, preferably strong enough to put a fair amount of force into. I used a hunting knife.
A small screwdriver, or toothpick for applying new thermal paste, or reusing thermal paste.
Step 1: The Feet
I don't think I 'Need' to say this, but make sure the power brick is Unplugged before servicing it.
Once the rubber feet are removed you will see a small plastic insert where each foot came out of. This insert can be pried out by pushing a blade between its edge and the power supply, and prying it up.
I ruined my first one by trying to use the good ol' dental pick, but I found that this hunting knife worked far better, and kept them in a reusable state.
Step 2: Screws and Covers
Get your trusty Phillips ready for action.
After you get the screws out, with the power supply still laying bottom up, pull on the bottom half of the plastic shell. It should come up with little effort.
The next thing you need to do is look for a single screw hidden down between the light and the output cord. This screw secures the heatsink to the PSU. Remove it.
There is also a very small, two wired connector for the PSU fan, you'll want to remove it as well so you don't tear it off. ;)
Once the screw and connector are off, grab the plastic shell, and one end of the power supply and pull them apart. It may take some effort due to the thermal paste holding the heatsink on.
Step 3: Heatsink and Cover
is to remove the metal heatsink from the plastic case.
There are two screws at either end, and a two in the middle under the plastic layer.
I do not recommend removing the plastic. I presume it is there for insulation purposes. Also try not to get anything mixed with the thermal paste, most of it is reusable.
Step 4: Cleaning the Fan, and Reapplying Thermal Paste.
Be sure to get all the dust off, and while your at it, make sure you clear all the dust out of the fins on the heatsink.
( note: When putting the heatsink back on, be sure to run the fan wire down the side of the plastic housing, and out the gap in the sink. )
To start putting it back together.. A good thing to do is take thermal paste that is still good, or new stuff if you'd prefer, and spread it nice and evenly over the parts that need to contact the heatsink.
I found LOTS of extra pushed out of the edges, so I simply dragged it back to the center and spread it around. A small screwdriver or toothpick works well for this.
When your done, stand the side of the case nice and close to the psu so you can PLUG IN THE FAN WIRE, then carefully press the case back on.
Reinsert the lonely screw that holds the sink to the PSU.
Step 5: Putting the Rest of It Back Together
Make sure the cord and plastic inlet are fitted into the case properly, drop on the other plastic cover, and tighten up the screws. Make sure they are fairly snug. Pressure between the power supply and heatsink makes for better heat transfer. Which means better cooling.
Take your plastic inserts, assuming they are still intact, and press them into the holes.
I mashed mine in with a screwdriver handle. Then mash the rubber feet back into place. They may take some convincing if the inserts were mangled.
Step 6: Admire What Ever It Is That You Just Did.
Make sure to keep it in an area where it can get some air, preferably off the carpet.
Heat shortens the lifespan of many items. ( and as many of us know, quite a few Xboxs have very short lifespans )