What are the different ways to sing in harmony? There are at least six.

Learning to create your own vocal harmony part along with a melody is often something that musicians learn intuitively, through listening to a lot of music, but also by singing in a band or choir. Having said this, there is nothing wrong with taking a short cut towards gaining this skill, by using a little musical knowledge. You can create vocal (or any other, for that matter) harmony parts, using some basic knowledge of harmony (certainly not as advanced as harmonising chorales in the style of Bach, but a good deal above the level of simply trying to find what "sounds good" with a trial-and-error approach

start with simple song

use music sheet

practice

sing a third up or down

sing a note in a chord

try out supensions