How do I write a harmony part, if I have a melody?

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Easy, just write notes on the 3rd and 5th note above the root. So, it the note is a “C” and your in the key of C, you can use “E” and “G” and it will perfectly harmonize. It can be a lot more complicated then that, but, thats a start for you….

If I were you, I’d find someone who knows how to do it, and work with them. There are a lot of nuances—major and minor chords and using the seventh and then there’s the issue of how the music flows.

If you are doing something simple, like rock, then you can get away with what @Atomic suggested. In fact, it may be as easy as going back and forth between two chords, or only using one chord. Rock music usually uses two chords and goes back and forth between them. Once you figure out which two you want, you just go back and forth between them for the whole melody.

If you’re doing anything more complex than that, I really think you need to learn more, preferable with a person.

You can do several different things, but I would suggest, tape-recording your melody, listening to it, then imagining, and singing the harmony yourself. Or, if you have a piano available, learn to play the melody, then find what harmonizes with it. It is amazing what you can do when you think you can’t.

I agree with @Myuzikalsoul. I often make up harmony parts while listening to the melody. Some things come more easily when doing them intuitively. One time I was handed a piece of music to play where the bottom line containing the bass clef was cut off. When I got to the bottom line, my left hand actually played the missing part, without me thinking about it. If I had stopped to think about what I was doing, I’m not sure I could have continued…