Changing chords is something you'll need to do a great deal as you learn to play the guitar. Beginners may think that they will never become proficient at changing chords, especially when they find that it seems really hard to change over even when using ?simple' chords. Don't be dismayed. So-called simple chords are not called that because they are simple to play. Most simple chords require quite complex finger movements.
While changing chords smoothly requires a great deal of practice, there are some things you can do to facilitate the movement considerably. One of the most important things is to relax. Many guitarists tense their shoulder and arm muscles when playing chords with the effort of finding the right notes in a hurry. The tension in the shoulder and arm translates down into the fingers and causes them to grip so tightly that it is almost impossible to change at all, let alone do it with speed.
Tension causes the fingers to press against each other instead of having space between them. This makes it difficult for each finger to move and find its string independently of the others. Tension also causes the hand to grip too tightly so that there is no space between the hand and the guitar. You cannot move your hand up and down the neck of the guitar swiftly and smoothly if you are grasping it for dear life. Worse still, a tight hand is a sweaty hand, which also hinders that smooth slide you need.
So be aware of tension in your left hand particularly and try a to keep it as relaxed as possible when bringing it to the neck of the guitar. The fingers should be held in a relaxed curl, separate from each other and a space kept between hand and guitar especially as it turns from a G to a C chord, which is one of the most difficult movements.
Another good idea is not to lead with your strong index finger. For the C chord, place your 2nd finger on the fourth string first. Keeping your hand out, place the 3rd finger next and finally the index finger on the 2nd string, first fret. Keep enough space between the index finger and guitar to stick a pencil through.
When practicing chords, start off slowly and work up to speed gradually. The world won't come to an end if you are not perfect in two days. Learning to relax for chord changes is the most important thing to do.