For example, in the intro to Snow by Red Hot Chili Peppers, the chords played are:
G#m - E - B - F#
in that order. How do I begin to realize the chord progression? Do I need to find the key first?
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You need the key to analyze a chord progression. The chords themselves will tell you the key and what type of progression, but first you need to make sense of the chords you have. If you know your keys pretty well and what chords belong to each key it is a simple task.
You have 3 major chords B, E, and F# and one minor chord G#m. The simplest way to figure out the key is find out what scale fits them best. Typically I like to figure out the distance in intervals between the roots of the chords. From B to E is a perfect forth, from B to F# is a perfect 5th, and from B to G# is a major 6th. From this and from what the chords qualities used the key you are in is B major/ G# minor.
The analysis for the progression in B major is vi, IV, I, V and the analysis for the progression in G# minor is i, VI, III, VII.
First you find the key, then you assign the chords to the degrees of the keys and try to see some paths made of degrees progressing. This will give you the bigger picture.