Learn the terminology of Gregorian notation. "Final" is the last note of a chant, "dominant" is the tone of the piece, and "mode" is the collection of pitches in a piece. Chant music has modes instead of key signatures. It also has no time signatures.
Learn square notation. Chant music is written with squares for notes, called neumes. Some of these notes have direct equivalents in modern notation, but some are specific to chant. A tutorial can be found in the Resource section.
Find the starting note. Chant is written on a 4-line staff and does not have a major or minor key. There are only two clefs in chant music, either a Do or Fa clef. The Do clef indicates where Do is by the line it appears on; the Fa clef indicates where Fa is on the scale.
Move the pitch up or down as necessary to accommodate your voice.
Check your pitch with a piano.
Join a choir. Chant music was meant to be sung by a number of people, so the best result will come from a group of singers performing a chant.