My two cents. Nothing more than what was said in the instruction example you gave. Perhaps seeing it in another format will help.
Sub-dominant chords like to move to dominant chords. Dominant chords like to move to
their tonic chord.
So using a sub-dominant chord (the ii or IV) - of the new key - as a pivot point will draw you into the dominant chord of the
new key and that dominant chord wanting to go to
it's tonic chord would be a good way of establishing the new key.
The following helped me understand what chords like to do. Just because they like to move a certain way does not mean they have to move that way. All of the chords in one key will sound good with all the other chords in that key. If we let them move how they like good things normally happen.
The I tonic chord, can move anywhere in the progression it wants to, but, in doing so you resolve the tension and return to rest. Do you want to return to rest?
The ii chord is a sub-dominant chord. It likes to move to a dominant chord.
The iii chord is the move somewhere chord, it normally drags the vi with in in the move.
The IV chord is also a sub-dominant chord and likes to move to a dominant chord. As the ii and IV share likes they can sub for each other.
The V is the dominant chord. Making it a dominant seven chord increases it's tension and it wants to move to the tonic chord right now.
The vi chord wants to move to a sub-dominant chord.
The vii chord is the diminished chord and on top of this it is also a dominant chord, however, is in no hurry to move to the tonic chord. It is used as a move somewhere chord as in a turn-a-round, for example; vii-iii-vi-ii-V7-I. Here also the V and vii share likes and can sub for each other. Want to resolve quickly use the V want to move somewhere as in a turn-a-round use the vii.
Move to the pivot chord - then let the pivot chord go - in it's key- where it likes to go..... would be an effective way to establish the new key.