How do the terms in 千里之行，始于足下 modify its meaning? I came across the phrase


  千里之行，始于足下


on the Internet. Per consensus from native speakers, it appears it can be loosely translated as 'the journey of a thousand miles begins at your feet'.

I'm able to understand what the nouns 千里, 足, as well as what the verb 始, are all doing in this sentence. However, what are the characters 之行 and 于，下 doing? Are they acting as adjectives, prepositions, adverbs, or something else? How does each character modify the preceding characters to arrive at the full meaning?
Actually your translation is a pretty verbatim one. I will give the word for word translations for each phrase and let you feel what parts they play.

千=thousand

里=miles

之=of

行=journey

始=start, begin

于=at, from

足=feet

下=under

Something to comment on: in chinese, “A之B” is somewhat equivalent to "B of A", meaning B is part of A, or B is described by A.