At many times in our history the repetition of sacred phrases has been recognized as helpful to a meaningful prayer experience. In my case I resisted a long time before trying any of this - some sort of fear kept me from it, as though I would die or something like that. Instead once I plunged in, each time the practice grew on me....like cultivating a taste for olives only much more special and valuable (forgive me, any olives that are reading this). Rabbi Shefa Gold introduced me to these practices, and I encourage you to seek out her work and teachings on the subject, she is a wise, authentic and safe teacher.
Below are the steps I have found most useful, read them through a few times before trying this for the first time.
l. Select a verse for chanting, (perhaps from psalms), study and think about what the words mean to you. (For example, before shabbat I often chant from Song of Songs "Kol dodi, hinei zeh bah" which means The voice of my Beloved, here! it's coming! This is a delightful way to increase anticipation and create a state of readiness to welcome Shabbat into one's life.)
2. Settle yourself into a comfortable position with a copy of the chant on the table or floor in front of you, (if it is not in your memory).
3. Take some time to gentle yourself; notice and follow your breathing.
4. Begin chanting the verse...either in a repetitive tone that is comfortable for you or a melody designed by a chant master like Rabbi Shefa Gold or one you develop for yourself.
5. Let yourself fill with the emotions evoked in you by the chant.
6. Gently set free any distracting or even interesting images or thoughts that enter your awareness. (I imagine they are hot air balloons and let them drift upward and out of sight in my consciousness....those less visual might imagine them as a sound like the whistle of a train that fades out of sight.)
7. Keep chanting, use regular breathing that starts deep in the abdomen. Boredom usually comes at some point, this is normal....push through it, keep chanting until you are at one with the chant, it's pouring through you is like the air you are breathing.
8. After perhaps five minutes or so, softly lower your chanting until you end it, don't continue the chant in the silence, but instead keep totally silent, breathing regularly.
9. Notice the vessel you have created with your chanting. You may be aware of being in a special place, certain colors or a sense of presence.....explore for openings, passageways, sounds, voices, new awareness or just great peaceful centeredness. Dwell in this place for as long as you can...it is a gift you have cultivated for yourself.
10. Choose to emerge by noticing your breathing again, send a blessing to God, ha-Makom, The Source, for constructing us so magnificently and sending us awareness and blessing.
11. Notice how long you took for this process....some of us will gradually stretch our duration (as runners do), others will want to contract it some, so as to refrain from excesses that impede doing mitzvot and other activities of daily living.
Rabbi Shefa Gold's website offers good examples of this form of chanting and I've found her workshops to be most excellent.