Listen to lots of recorded or live music, especially classical music. This may not be your favorite genre, but classical music, Mozart in particular, has very clear and logical harmonies. The first step in learning to sing on pitch is learning to hear pitch. Pitch is easiest to hear surrounded by sweet harmonies.
Get yourself an instrument, preferably an acoustic guitar or piano. Stand quietly and try to feel the vibration in your ear and in your body. Getting accustomed to feeling the pitch will help you hear the pitch.
Play a note or even better a chord on your instrument. Playing a chord with the note you want to sing will help your ear hear the note better. Remember to also try to feel the vibrations of the chord.
Now, sing the pitch, keeping the harmonies of the chord and feeling the pitch in mind. Have someone else listen to you or record yourself. Were you on pitch? Do you need to aim the pitch a little higher or a little lower? Adjust the pitch and try again. Once you are on target, try to repeat it.
Practice, practice, practice. Repeat this exercise every day for 5 to 10 minutes. But remember, Rome wasn't build in a day. Be patient with yourself and give yourself at least two weeks of practicing before you decide whether you are tone-deaf or not.