Modulation Using Common Chords
Another form of modulation (which is much simpler than the first way) is to use a transition chord that is a part of both keys. For example, let’s say that we want to start out in C major and end in F major. The easiest way to do this, is to write out all of the chords on both keys so you can see which chords are common to both keys.
C Major - C Dm Em F G Am Bdim
F Major - F Gm Am Bb C Dm Edim
C, Dm, F, and Am are all common chords in both progressions, so any one of them (or several of them together) could be used to transition from one key to the other.
Here’s an example I came up with, with the chord numbers underneath for both keys:
Notice how the progression flows seamlessly, yet you start out in C major and end up in F major. Am and Dm work as transition chords because both of them are in C major and F major.