Recently I've started trying to harmonise when singing in church, as the only place I regularly sing with a large group of people. I'm finding it really hard and I wondered if anyone can suggest how one might approach learning how to do this.

It sounds beautiful (to me) when you here people throwing harmonies in ad-hoc and it's specifically this kind of improvisational harmonising I'm interested in, not preparing/learning harmonies.

Congregational songs typically are pretty narrow and easy in range which means there is often scope to go down as well as up from the melody.