I would never open up the camera and try to clean the sensor on my own. There’s just too much of a risk.
Cleaning the lens, on the other hand, is something that you can do at home. Just get a clean, dry, lint-less cloth (like a microfiber cloth) and rub the lens. If you just apply a bit of pressure, and some elbow grease, your lens will be clean and unscratched, like new.
You can use canned compressed air to clean the dust off the sensor. Don’t rub it or touch it. A can costs about $3 at the camera store and will probably last for the rest of your life. Go for it.
I would take it in to a camera shop, I took my DSLR into a small privatly owned store that specialise in SLRs and they did a fantastic job at cleaning the sensor. No dust visable in the photo’s even at F22. It only cost me about $50AUD so it was well worth it
@simpleD You’re right. There are cans that leave a residue. I go to the camera shop (Rowe Photo) to get the good stuff. $3 instead of $2. It doesn’t leave a mark.