best way to get good at harmonies is to develop you ear. lots of ways to go about it.
to get started - play a simple chord progression and sing any note you hear in each chord. sing only one note per chord. try to keep the line smooth ,not jumpy. then, with the same chords, start singing on a different note and do the same thing. the resulting lines should harmonize, provided you sang notes within each chord. do this a lot and your ear will pull harmonies out of everything.