>>what *exactly* do i need to learn in order to understand music theory and transposing. i want to >>avoid *wasting time* learning theory i won't really need.

Why are you so worried about wasting time? And, since you don't know anything about music theory, how would you know what you need and what you don't need?

I once had a student who got angry because I was teaching him to play quarter notes--he said, "Those are to simple for me!"

Anyway, here is what you need to know in order to transpose:

The names of the all 12 notes--

The names of the notes, including sharps or flats,in each key signature--

The Major, absolute minor, and relative minor scales for each key signature--

The Tonic, Supertonic, Mediant, Subdominant, dominant, submediant, and subtonic triads in each key--

Once you know that stuff, all you need to know is that, to transpose, you can just substitute the Tonic, Supertonic, Mediant, Subdominant, dominant, submediant, and subtonic triads(and notes) in old key, for the Tonic, Supertonic, Mediant, Subdominant, dominant, submediant, and subtonic triads in the new key--

Of course, it helps to know about accidentals and the circle of fifths, because you want to avoid confusing, say, the Dominant Second Chord with a supertonic chords--

A simple trick is to make a little table :just to write out the scale for the original key, and then write the scale for the new key right underneath it--then write out your chord progression in the original key, and then write the new chords right underneath them, using the table.

You can transpose the melody, note for note, the same way--Simple, isn't it?