Before you begin the exercises below...
...it is helpful to remember that when you practice making the move between chords you are really practicing the move itself rather than focusing on the final positions for each chord. It's like learning a dance step. If you take the time to clarify the particulars of how each finger moves and then how to orchestrate and practice the bigger picture of the hand and finger motion working in concert, then practicing precisely, slowly and patiently will gradually ingrain the correct movements into muscle memory so that your moves while changing chords will become smooth and easy.
Moving between C and F open chords on Guitar
Please note that the little finger is not used in either of these chords, rather it is shown in proper finger position since this position is desirable to always be ready to use it immediately as needed.
Moving between chords while strumming.
Before beginning this first exercise to learn to move between Em and A(add2) take the time to plan out which fingers will play which notes in each chord and how best to plan the move between for maximum smoothness and efficiency.
With these two chord shapes I advise using finger 2 (middle finger) and finger 3 (ring finger) for each chord. This will allow you to make other adjustments for chord shape variations as needed in situations you will encounter as you evolve. To play the Em chord, finger 2 is on the 2nd fret of the A string and finger 3 on the 2nd fret of the D string. These will simply move in tandem to the 2nd fret of both the D and G strings for the A(add2) chord.
Practice making this move a few times before playing the exercise as shown in the graphic. You'll want to move as if in extreme slow motion at first to carefully coordinate your movements to be as smooth as possible. This will coordinate your muscle memory to maximum efficiency.
To do the exercise, strum the Em with a down stroke, then as you do the upstroke on open strings that follows (noted as N. C. to represent "No Chord"), move your fingers towards the position of the A(add2) chord in slow, smooth motion, timed so that you place your fingers on the strings just as it's time to do the down stroke for that chord. Then, as before, you move during the upstroke while playing open strings during the move and time your placement of the Em chord to coincide with you down stroke. The process repeats enough times to make some progress towards improvement.