How we cite our quotes: (Line)
Quote #1
A broken ALTAR, Lord, they servant rears
Made of a heart and cemented with tears (1-2)
We know the poem is in the shape of an altar, so we know the "broken altar" refers to the poem itself. There's definitely some irony going on here because the poem is carefully and artfully arranged, which means it's definitely not broken.
Quote #2
Whose parts are as thy hand did frame;
No workman's tool hath touch'd the same (3-4)
Well, it sounds like the altar is "broken"—through no fault of the speaker. All the "parts" that make up the poem are just the way God made them. The speaker isn't responsible here as everything he has used to compose his poem comes from God.
Quote #3
Wherefore each part
Of my hard heart
Meets in this frame
To praise thy name (9-12)
"Frame" refers both to the metaphorical altar the speaker has been talking about this whole time but also, of course, to the poem itself. If all of his "heart" meets in the "frame" that is the poem, then we can definitely say he has put his all into composing this poem and using it to praise God.