Just as we did to locate the Root note of the V chord, the G major tonic triad also contains a major 3rd, the note B.
We can use this as the Root note for the iii chord which, in the key of G major, will be B minor.
When a chord progression moves up or down a third (with the Root notes spanning three alphabet letters) there will be some overlap of the notes contained within each triad. Therefore only one note is different between the two chords.
G = G-B-D
Bm = B-D-F# (B is a minor 3rd above G)
D = D-F#-A (D is a minor 3rd above B)