Watch the Economy of the Left online guitar lesson by Brad Carlton from Chord Studies: Inversions Vol. 1

This example involves two different chords in a four bar progression.  Each chord gets a full measure.  We'll change from Dm to C on the second, third, and fourth strings in the first two bars, then switch to the third, fourth, and fifth strings for the final two chords C and Dm.  For your first chord keep your index finger free from fretting notes, that way you can keep it in place for the barre in the upcoming C chord.  This is a concept you want to look out for in all chord changes, to create good smooth economy of motion in the left hand.