The poem is called "metrical feet," and it talks a lot about – gasp! – metrical feet (i.e., the small units that make up a line of verse). Even though it talks about different types of poetic meter, the poem also playfully employs the language of things you do with your actual feet – walking, leaping, bounding, jumping, and so on. The poem is about both feet and feet.
Line 1: The speaker talks about the trochee. Trochees don't literally "trip," so that word is here a metaphor to describe their movement from "long to short." You might also think of it as personification because the speaker is giving a human action – tripping – to a nonhuman object. Prepare yourselves, because Coleridge is gonna use this one quite a bit.
Lines 2-4: The speaker describes the spondee, which, of course, can't actually "stalk" "in solemn sort." And they definitely can't actually chase after dactyls ("come up with") so both "stalk" and "come up with" are metaphors for the spondee's slow, plodding movement. The repetition of the letter "s" in six straight words, and the repetition of "l" in "long to long," is called alliteration.
Line 5: We meet the most famous English foot of all in this line: the iamb. Iambs aren't real, in the way that people are, and so they can't "march." This is a metaphor that's meant to show us the regular, regimented movement of the iamb.
Line 6: The speaker discusses the anapest. Like the preceding types of feet, anapests don't really "leap" or "bound," so these are also metaphors to describe its quick movements.
Lines 7-8: We now learn about the amphibrach. Like its companions in the poem, it can't actually "do" the things the speaker says it can ("hastes with a stately stride"), so this is also a metaphor to explain the way it kind of sounds. Are you getting the hang of this?
Lines 9-10: The speaker discusses the amphimacer in lots of colorful language. The amphimacer is compared to a "thundering" horse. Comparing two things using the word "like" or "as" ("my love is like a red red rose") is called a simile. Just remember it like this: it's like a metaphor, but different (hey, that's a simile too!).
Line 13: The speaker talks about "these meters." He could be referring to the poem itself ("these meters I've written" or "these verses"). If he is, this is an example of synecdoche, which is when you use a part to stand in for the whole (as in the phrase, "all hands on deck," where "hands" stands in for "workers" or "people"). The speaker could also be referring to Derwent being knowledgeable about "these meters" (i.e., the ones discussed in the first stanza) in the future.
Line 17-18: The speaker says that, if Derwent could stand on the top of Skiddaw (a really tall mountain in northern England), he wouldn't see anybody that loves him as much as his father. The rhyme on "whole ridge" and "Coleridge" is called a hudibrastic rhyme (bust that out at your next cocktail party if you want to sound really smart). It is a rhyme in which a word with multiple syllables (like Cole-ridge) is rhymed with several words that only have one syllable (whole ridge).