How difficult is it to clean the sensor on DSLR?

I have a digital SLR camera and the sensor has dust on it that I cannot remove with the standard air duster. I have heard the sensors are very fragile and that you should have them professionally cleaned, but I have also heard from some that it is fairly simple. I think it is $50 to have it done where I can get a kit for that same price that would allow me to clean it a few times. I'm fairly good with handling electronics and working on things so I think I could manage it, but I don't want to mess it up.