I have a few tips.
1. If you really want to understand how to get proper exposure, using a single type of camera or meter will help you.
2. Do NOT use any sort of matrix metering, as it is impossible to know how it meters any given scene. Full-field, center-weighted or spot metering will allow you to understand how the meter of a given camera works.
3. Shoot slide film. You will have a very clear indication of how your exposures have been. If you are off by even a third or half a stop, it will be apparent. Try bracketing 1/2 or 1/3 of a stop...it will allow you to see the difference.
4. If you have time, look at a given scene and try to guess the exposure. Then when you see the meter's advice, you will know whether you were close. If you keep doing this, you will learn to guess exposure fairly well.
5. When using a center-weighted or spot meter, learn what types of common features give correct exposures. For example, if you point it at grass in daylight and see whether that gives you proper exposure or under/overexposure. Pavement or concrete are other good examples...brick walls, your hand, people's faces, the ocean etc. You can eventually learn to judge object's luminence so that you can point the meter at something about 18% gray and get an accurate reading.
5. Another trick with a center weighted meter is if you have a very bright and very dark area, you can often put a portion of both in the metering area and get a good reading. An example of this would be a shot of the ocean...the sky will be too bright and the ocean too dark, but if you put the center weight meter at the horizon, the upper half will be sky and the lower ocean, so the exposure will balance out. You can use this principle in many different cases.
Anyway, these are just a few tricks. I learned photography on slide film, and I think it has really really helped me in getting good exposures. Negative film is great, particularly black and white, but it can make you very sloppy.