The best way to move smootly from chord to chord is to use a note(s) from the previous chord. This means that if 2 chords have at least one note in common, keep your finger on that note for both chords, then move your other fingers for the rest of the chords. Here is an examle using the 1-4 progression:
Key C LH/RH
C / C-E-G
F / F-A-C
(repeat)
Now, those are root position chords, and in order for you to play those chords as they are written, you have to jump to each chord. Now, let's look at how we can use inversions to avoid jumping for each chord:
Look at the first 2 chords: C-E-G & F-A-C What note(s) do they have in common, if any? Answer: C Let's play those 2 chords, but keep a finger on C for both of them:
C / C-E-G
F / C-F-A
You see that? There was no jumping from the 1st chord to the other one because we didn't go anywhere. Now, that's if you are starting with a root position chord. What about a 1st inversion chord? Well, we can do the same thing:
C / E-G-C
F / F-A-C
You see that? We still kept 1 finger on C and everthing else moved. So, not only does it work for root position chords, it works for any inversion of the chords, as long as they have at least 1 note in common.
That's basically the idea of it. In the event that you come across 2 chords that don't have any notes in common, then you should use the closest inversion so that you don't jump too much.
