C

Let's review the shape fragment we referred to earlier as being common to both D and G major. We'll use this same two-finger shape as the basis for the chord forms C and F. 

First, get familiar again with the D major form. Practice again, changing from D to G and back. 

When in the G position, your ring finger is on the sixth string, third fret, your middle finger on the fifth string, second fret, and your pinky on the first string, third fret.

To get to C, remove your pinky from the first string, leaving the other two fingers on the fret board. Move them each towards the floor as you hold your guitar, so your ring finger is on the fifth string, third fret, and your middle finger is on the fourth string, second fret. Already your index finger is in the air somewhere around the first fret. Put it on the second string, first fret and there you go, C major. 

Practice some chord exercise to work out the glitches when changing to C from other chords. G to C is a little easier, D to C a little more difficult. So is A7 to C a little more difficult. Begin your strum in C from the fifth string, begin your strum in G from the sixth string:

G    G    C    C

C    C    G    G

Repeat for a minute or two. Or three. When you are satisfied you can remember where your fingers are supposed to go by looking at them, and not a chord picture on a page or screen, you've done something. 

Begin your strum in C from the fifth string, begin your strum in D from the fourth string:

D    D    C    C

C    C    D    D

Practice each exercise again, this time listening to the sound. Work at fixing up muffled or buzzing strings. Work at being able to change chords right on the first beat of measures three and seven. If you can't, slow down to a tempo you can handle. Speed will come. Next cut the duration of each exercise from eight measures to four, like this:

G    G    C    C

G    G    C    C

And:

D    D    C    C

D    D    C    C

Spending five or ten or fifteen minutes at this sort of thing is a long time. But five or ten or fifteen minutes is all it takes for your fingers to begin remembering the positions. With that, the speed and accuracy of your chord changing will improve.