Although good DSLRs have sealed bodies and often a sophisticated ultrasonic cleaning mechanism on the sensor, you'll anyway run in dust problem after some time. This time interval could be very long, since dust enters when you change lens, and many people use always the same zoom. But if you have many lenses, and you take many outdoor pictures, dust will inevitably lay down on your camera sensor.

Step 1: The Swarm of Flies

Effects of this bad attitude of dust are not much noticeable, but when a bigger dust grain will come to keep company to his fellows, you'll notice it and you'll probably want to close aperture to 22 or more and take a shot to the sky. Then you'll become frighteningly aware of the affair magnitude!
I knew dust was becoming a serious matter for my dslr, but I took this shot for curiosity during my last travel on mountains, you can imagine my astonishment when I've seen a swarm of flies around the sky in my picture!

Step 2: The Ingredients

I've already cleaned with success my Canon 1D APS-H sensor, which is bigger than the APS-C sensor of my 40D. The bigger is the sensor, the more easy will be the cleaning process. Of course you can bring your DSLR to the nearest photography shop and pay for a professional service. That will be undoubtedly the easier and safer way.
If you decide to go through the diy way you'll need a few tools:

a phial of ethyl ether
some paper tissue free from silicone to clean optical glass
a dropper
a lancet handle
a plastic card like a credit card

To choose the right type of card, you have to check that ethyl ether will not melt that material. Indeed ethyl ether is a very powerful solvent, and it will dissolve many plastic and rubber types. The reason why you need this solvent is because it's very volatile and, if you'll act wisely, it will not submerge your sensor and the circuits below.

Step 3: The Main Tool

Cut the card to make a sort of spatula/squeegee, which has to be as wide as the sensor height.
The back side of the spatula will be inserted in the lancet handle, so cut it of the right shape.
To check if ethyl ether will dissolve the card, pour some solvent in a little container (a glass one, or use the same cap of the ethyl ether phial) and let the spatula submersed for half minute, then rub it on a clean glass to see if it leaves some remains. The glass should remain very reflective.
You have to be very careful to not let the liquid going into the nipple of the dropper, because since it's made of rubber, it will dirty the solvent and then your sensor!

Step 4: Moping Up

Found the right spatula, wrap a double stripe of cleaning tissue on it. The paper has to be kept in place by the same metal handle head, because you can't use any type of adhesive tape, an elastic neither, since ether will dissolve the glue or the rubber, and you'll ruin the sensor.
Pay attention to not touch the paper too much with your fingers, and not touch it at all when solvent is applied, because it will dissolve finger oil and deposit it on the sensor.
The lenses cleaning tissue should be enough soft to avoid scratching the surface of the sensor. Indeed the outer layer is a very hard plate, which could be possibly scratched by a metal dust grain, but not by the paper sheet.

Step 5: Reveal Your Heart

To raise the mirror of the camera you have to search the "manual cleaning" property in the menu. This will keep the mirror lifted up until your battery has power. This is the reason why usually DSLR cameras don't let begin the process with half charged batteries.

Cleaning the sensor by yourself is not difficult, but it needs a lot of perseverance. You have to pay great attention to some rules to avoid permanently ruining your DSLR, nevertheless the danger to lose your beloved camera is always present. For this reason I suggest you to test the process on an old camera body, and anyway don't make it on an expensive new camera, where the cost of the professional service would not be high compared to the camera value.
My lovely 40D is old enough to take the risk, and I've already cleaned a DSLR sensor a pair of times to feel pretty confident.

Step 6: The Solvent

Drop some ml of ethyl ether in the cap (or the little glass container) so to be able to immerse the extremity of the spatula with wrapped tissue. The ethyl ether is so volatile than it will disappear from the cap in a pair of minutes. It also will vanish from the bottle in few hours if you don't close it each time.
After dunking the tool in the solvent, you see that paper absorbs a quantity of liquid. That quantity varies depending of the number of paper layers you used on the squeegee. I used two layers and it seems good to me, with that setup I usually wait about 5 seconds to let the excess of liquid evaporating, then with the tissue still wet, I proceed with the cleaning pass.

Step 7: The Pass

Since the dimension of the cleaning tool would be the same of the shorter side of the sensor, you'll have not to worry about the side trace left after the pass. Anyway you'll have some complication with the accumulation of dust and remains at the end of the pass, exactly the same matter you'll run into cleaning a window with a rubber squeegee. Please pay attention to next rules:

make the pass at the right time, when the paper is wet but no drop could fall down
move the squeegee from one side to the opposite one as in the picture, in a single constant movement
try to reach the far end, which should be a very thin area out of the sensor active zone
after one pass turn the spatula, dunk it, and make the same with the opposite side of paper, this will avoid that dust grains scratch the surface
after these two transits change paper stripe and make it again, until you're satisfied with the results

If you see bad traces over the sensor don't freak out, until you don't drown the circuits or you don't engrave a Zorro initial on the surface you'll be able to clean almost perfectly your sensor!

Step 8: Pride Yourself!

When ,looking a reflection on the sensor, you see no more dust or bad traces, it means it's time to insert the lens and take the test shot.
As usual, set the highest value for aperture, point on an uniform surface, take the shot and check dark spots with the 100% zoom level on the display. If you notice something bad, keep in mind that image is specular, so if the dust grain is at top right of the picture, go looking at the lower left corner on the sensor.
My final image is not perfect, I'll work on the sensor again when I'll have time, but of course it's much better compared to the flies swarm of step 1! ;-)