Get out a vacuum cleaner. Turn it on and start cleaning the carpet. The vacuum cleaner emits a singular, sustained tone that you can try to match up with your singing voice. Even if you are an accomplished singer, this will help you tune up your ear even more. You can do this with a tuning fork as well.
Match the pitch. Try to sing the same pitch the vacuum is humming. If you are not on the right pitch, you will feel a vibration in your throat. These are harmonic sound waves. The waves will be wider (further apart) if you are further away from the note.
Fluctuate the pitch. Try to tune it up. Raise or lower your voice (just slide your voice up and down and don't try to be precise) and feel the vibrations. If they are getting faster, you are getting closer to the note. It will feel like your voice is battling with the hum of the vacuum. When you find the note, the vibrations will cease and your singing tone will feel relaxed and effortless. If you find this relaxed zone as your vibrations are getting wider, you have found a harmony note related to the tone. That's another lesson. Work your way back to the fast vibrations and then to the right pitch.
Exercise your ear. This method trains your ear by enlisting the help of your body to "feel" the tone.
Practice often. Do this little exercise every time you vacuum and it won't be long before you will see improvement in your ability to hear and sing the right notes. Once you get good at this, you can graduate to singing with other types of sustained notes on other instruments. Do it with a friend. Have him sing a steady note and you try to match it. Play a note on an electronic keyboard. The hardest instrument to do this with is the piano. The note doesn't sustain long enough for a beginner to use it, but as you advance, you can match your voice with the piano.