I need help understanding the structure of the poem "Pet Panther" by A. R. Ammons. I think I am understanding him correctly in that he is using an extended metaphor (conceit metaphor) to compare his attention to a wild animal. I think the poem is free verse—it has 5 stanzas and 20 lines. I don't know if I am on the correct track, and I don't know how else to explain the structure of the poem.

You are indeed correct that Ammons uses an extended metaphor to compare his attention to a wild animal, and you are also right that the poem is written in free verse, meaning that it has no regular rhyme scheme or syllabic meter. Often poems are written in free verse to produce a more natural, conversational, spontaneous tone.
One other point that you might make about the structure of the poem is that it begins with a problem and ends with a solution. The problem is how the poet will manage his attention, which left unmanaged will "pommel the / heart frantic," and "dislodge boulders." The solution the poet offers is that he will try to tame his attention and make it "lie down" within himself, where he says there is as much for it to focus on as there is outside of himself.
You might also look, in terms of structure, at examples of repetition in the poem. For example, the phrase "it will" is used four times in the poem in reference to the tendency of the speaker's attention to do as it wishes. Interestingly though, this phrase is used four times in the first three stanzas, but not at all in the final two stanzas. This reflects the fact that the final two stanzas focus on the speaker's efforts to tame his attention.