Changing from one chord shape to another can be hard at first. You have to develop your muscle memory, so that your fingers learn what they have to do without looking at them. Try to also think about what you are doing, to help the learning process. Looking for similarities between chords also helps.
You can sometimes use different fingerings for the same chord. This can make the change to the next chord easier.
- Example: when changing from E minor to E major, you usually want to use 2nd and 3rd finger for the minor. This way the first finger can fret the 1st fret on the G string. But, if the next chord is an Am, the change is easier if you use 1st and 2nd fingers for the E minor. This is because that way you already have the 2nd finger ready for the A minor shape, and you don't have to lift it at all.
Vertically movable chord shapes
There are some shapes where you can move from one set of strings to another to get a different chord. The quality of the chord changes though.
- Example: E major → A minor; fingers hold the same shape, but move from the 5th, 4th and 3rd string to 4th, 3rd and 2nd string. Similar: Esus4 → A, A → Dmaj7, Amaj7 → D7