Many traditional songs are harmonized with I, IV, and V chords. These are the first three chords that many people learn on the guitar, and the dominant (V) to tonic (I) progression is strong. The IV chord mixed in gives some variety.
Decide on a key for your song. Play the I, IV, and V chords on a keyboard, guitar, or ukulele, or work out a system using some automatic accompaniment system or loop library like Band in a Box, Garage Band. Some digital keyboards have these functions built in. There are also some online tools like the online groove generator at wholenote.com, where it is recommended to use Firefox or the Chrome browser.
Try a variety of chord tones, neighbors, and passing tones when constructing your melody.
Chord tones are members of the chord that is being used for the accompniment at that point in the song.
A neighbor is a non-chord tone that is approached from a chord tone, and is followed by a return to the same chord tone.
A passing tone is a note in between two chord tones.
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