There are several different ways and products to clean the sensor - whatever you do, do not spray the sensor with canned, compressed air. Otherwise, there are bulb blowers, static brushes, cleaning solutions, etc. Visible Dust products come to mind, and I am sure there are others. The technique depends on the camera body, but usually you remove the lens, go to the menu choice for sensor cleaning, which locks up the mirror, and away you go. You need a fully charged battery or, as the manufacturer usually suggests, an AC adapter to do the cleaning so the power does not get interrupted to the mirror lock up while you are cleaning the sensor, otherwise if the mirror comes down while you are poking around in there, the camera can sustain damage.
To get a good shot of the crud on your sensor, take whatever lens you would like, put it at f/22 and shoot an image of a clear sky (i.e., no clouds or other features that could hide the dust spots). This will show you all of the crud. After you clean, shoot that image again to make sure you go it all.