To make it simple:
Shutter speed and aperture are linked. You close one stop, then you have to set one speed slower to keep the same exposure, and vice versa. For instance 1/125 at f4 equals 1/60 at f5,6 (1/60 lets light in twice as much as 1/125 but f5,6 reduces an equal amount of light coming in from f4)
Depth of field is more tricky. It depends on the lens you use, the distance between you and your subject and aperture. Just to keep it basic.
Wide-angle lenses have more DoF than telelenses. Also, the closer you are from your subject, the less DoF you get. A small aperture (f11, 16, etc) will increase DoF.
John is right, get a good book on the technical aspects of photography or just browse on the internet.
Good luck!
