Learn basic Latin pronunciation using a pronunciation guide. Gregorian chant is entirely in Latin, and while you don't need to understand the language, you do need to know how to pronounce the words, as they differ from English.
Learn modal scales by singing and playing the scales on your piano. The modal scales are a set of medieval musical scales which differ from the familiar major and minor scales we hear in music today. The modal scales used in chants are Ionian, Phrygian, Lydian, Mixolydian, Aeolian, Locrian and Dorian. Use Latin vowel sounds when you sing the modal scales.
Download free Gregorian chant sheet music. Proper Gregorian chant sheet music has no key signature or time signature. There is no consensus on how to properly time Gregorian chant, but using your knowledge of which Latin syllables are accented is useful. Generally accented syllables are held longer than unaccented syllables.
Play the Gregorian chant on piano and sing the lyrics. After you have successfully completed a selection with the piano sing the selection again solo.
Find other singers through your local church or college, which often have chant choirs. If your college only lets students join choir groups ask to audit the class for free, meaning you'll attend for no credit. E-mail the the music director of your church or college asking for information on local Gregorian choral groups.