Sometimes when changing chords, there are little short cuts we can use that makes life a whole lot easier for us.
When changing chords, you want to look for any shared notes that exist. When I say shared note, what I mean is a note (or possibly more than one note) that exists in both chords and is held down by the same finger.
A great example for this is when changing from A minor to C major (both using open chords):
Notice that with these two chords, the first and second finger are in the exactly the same place. The only difference between these two chords is the position of the third finger.
So when you are changing between these two chords, the only finger that you need to move is the third finger, the first and second finger can stay in exactly the same place. A common mistake beginners make with this chord change is to take all three fingers off the guitar, rather than using the method outlined above, where you only move the third finger.
You can apply this technique to many other chord changes. This is just one of many strategies that we use to help you speed up your chord changes.