Below is an audio file of the easiest way, in my opinion, to chant the canticle.
As you can see in the pagescan from the 1940 Episcopal Hymnal below, I’m chanting #656, a setting written by S. Wesley.
Note verse 5!!! Instead of going back to the beginning of the tune, you repeat the second half at verse 5. So, verses 4 and 5 sound the same, before you go back to the beginning of the tune at verse 6 and proceed as normal. (This is why verse 5 is indented in the Advent 2017 Daily Office Booklet.)
Here’s the “Chantable” Text of the Magnificat:
My soul doth magni|fy the Lord,
And my spirit hath rejoiced in | God my Saviour.
For | he • hath regarded
the lowliness | of his handmaiden.
For be|hold, from henceforth
all generations shall | call me blessed.
For he that is mighty hath | magni•fied me;
and | holy is his Name.
And his mercy is on | them that fear him
throughout | all • generations.
He hath showed | strength • with his • arm;
he hath scattered the proud in the imagi|nation of their hearts.
He hath put down the mighty | from their seat,
and hath ex|alted • the | humble • and meek.
He hath filled the hungry with | good things;
and the rich he hath | sent | empty • away.
He remembering his mercy hath holpen his servant | Israel;
as he promised to our forefathers,
Abraham and his | seed for ever.
Glory be to the Father, and | to the Son,
and | to the Holy Ghost;
As it was in the beginning, is now, and | ever shall be,
world without | end. Amen.
Please let me know if you have any questions about chanting the Magnificat. I’m no expert, but I’m happy to help!