Play a single note on a synthesizer or piano. Try to sing that pitch.
Listen for a beat frequency. If you are completely in tune with the note, your voice and the tone together will combine into one single tone. If you are slightly too high or too low in pitch, you will hear a beat frequency--a slight wavering in the pitch. Raise or lower your tone slightly until the beat frequency slows and stops.
Repeat the same step with scales. Use programmed midi scales (see Resources below), or recruit a friend who plays keyboards. Start by singing along with simple major scales.
Progress to singing along to more difficult things. Practice minor scales and arpeggios.
Record yourself singing along to songs you enjoy. By this point, you should have a decent sense of pitch, so you should be able to listen to your singing and see how close you are to correct pitch.