By starting to use your camera in M mode, you have probably learned more about exposure in 6 months than many people will learn in 6 years.... well done.
In P mode, if you wish to over or under expose you use the exposure compensation. Press the button on the back of the camera and dial in + or -. The good thing is that your old friend the EV bar will appear to tell you how much compensation you have dialed in.
One thing to remember is that in lighting situations you describe, it sometimes is not possible to have the shadows perfectly exposed without the highlights "blowing out" This is not a fault of your technique, but a fact of the science of photography.
Have a look here for some good tutorials on exposure
Cambridge in Colour - Digital Photography Tutorials & Gallery
I tend to use AV (aperture priority) most of the time.