Good point on the use (or rather non-use) of compressed air in any form, and as was mentioned, the Giottos rocket is ideal, particularily the new version with the angled nozzle.
The first thing to remember is that you're not cleaning the sensor, you're cleaning the high-pass filter in front of the sensor. This is in fact, relatively hard to damage, despite what some people would have you believe. It is easy to streak however, so wet solutions should be used with caution.
First, remove the lens, and lock up the mirror and open the shutter (if req'd). Then with the camera held upside down at an angle (so that the lens mount/opening is facing down, but not directly down, use your blower bulb to blow out the mirror chamber. Get the tip close too (but don't touch) the high-pass filter.
If that doesn't work, then you will likely need to go to a sensor brush. Big Mike suggested the Arctic Butterfly (
www.visibledust.com) which I highly recommend. I've used one for about three years now, and while expensive (~$100) it works VERY well. If that doesn't do the trick, then you need a wet solution. Once again, I recommend the Visible Dust products (No, I don't work for them, but their products have never failed me).
The wet solutions are the ones to be used with care, and EXACTLY according to manufacturer's directions. Otherwise you may wind up with streaks and smears which will be an absolute <female dog> to get rid of.
I have seen all sorts of suggestions on-line for using such things as masking tape, and other adhesives, isopropynol alcohol, and other 'creative' tricks. I strongly advise against using any of these.
If in doubt take the camera in and have it done by a professional, but if your camera doesn't have a built-in sensor cleaning system, you should learn how to do it yourself, it's not difficult.
Good luck!