Separate chord identity from note order
A C major chord still contains C, E, and G when E or G becomes its lowest note. These reordered forms are inversions. On piano, inversions let you connect chords without moving the whole hand to a new root position every time. Play C, E, and G, then E, G, and C above, listening to the familiar harmony in a different arrangement. Notice the top note as well as the bottom, because the upper voice can become a noticeable line in your accompaniment.
Find the smallest useful movement
Try C major followed by A minor. Keep C and E where they are and move G to A. Next, find an F major voicing close to that position. Do not insist that every note move by the smallest possible interval if the resulting hand shape is uncomfortable. Aim for a natural connection that you can repeat without tension. Practice the right hand alone, sounding each chord as a block and listening for a smooth top line rather than watching only the fingers that change.
Add a clear bass reference
Play a single root in the left hand at each change while the right hand uses its nearby inversions. This can preserve the intended bass direction even when the lowest right-hand note is not the root. Check slash chords separately, since they may specify a different bass. Follow a verified chart for the progression and keep the rhythm plain until the notes are secure. Finish by humming the melody over the accompaniment. An inversion is useful when it supports the phrase, fits your hands, and avoids unnecessary leaps, not merely because it looks more advanced than root position.