Write down the lyrics for your chant. Gregorian chants are most often sung in Latin. One option is to find a poem or prayer in Latin that you like and use this as the basis for your chant. Your lyrics can be religious, but do not have to be.
Write a melody for your lyrics using one of three types. The first is syllabic, in which each syllable has a note; the second is neumatic, in which each syllable has two to three notes; and the final and most complex is melismatic, in which each syllable has six or more notes.
Use a piano or any melodic instrument you are comfortable with to play and experiment with your melody, and write the melody you come up with on staff paper, along with the lyrics. You can write variations on both the melody and the lyrics in your composition, which is known as "free melody," or you can vary the melody with the same lyrics, which is called "recitative."