First and foremost, The Rime of the Ancient Mariner is one of the best representatives of the English ballad tradition. A ballad is not just a kind of song that people slow-dance to with the lights dimmed. No, in poetry terms, it's a kind of poem that tells some kind of narrative or story, often a lengthy one.
This poem was included in the collection titled Lyrical Ballads published by Coleridge and William Wordsworth in 1798. Unlike some of the other works in the book, this one is actually more ballad than lyric. The phrase "lyrical ballad" was supposed to signal the authors' intention to smoosh together two different genres: the lyric, dedicated to personal experience and emotion ("Ah, it's a dark and dreary day in my soul!") and the dramatic poem, which has characters and a story ("And then Tom went to Suzie's house"). With the intensity of its descriptions and its sheer emotional force, The Rime of the Ancient Mariner does feel like a lyric at times. But really, it's a story.
Coleridge borrows the form of this poem from old, popular English ballads like "Sir Patrick Spens." Most stanzas have four-lines, called a "quatrain," and a rhyme scheme that goes ABCB, so the second and fourth lines of each stanza rhyme. Of course, not all of the stanzas have exactly four lines: Coleridge isn't willing to sacrifice meaning for form.
The line lengths alternate between eight syllables in the first and third lines, and six syllables in the second and fourth. The meter is characterized by a lot of iambs, the most common metrical unit in English. An iamb is a short beat followed by a long one, or, if you prefer, an unaccented syllable followed by an accented one:
Be-low the church, be-low the hill,
Be-low the light-house top.
So, basically, what you need to know about the form of this poem is that it takes older forms and updates them with all the flashy, stormy elements of Romanticism.