You stop unwanted sound by muting with both hands.

With your picking/strumming hand use the side of your palm to mute in between chord changes.  With your fretting hand try to remain in contact with the strings as much as possible.  Release the pressure required to change positions, but remain in contact with the strings in order to keep them from sounding.  In some cases it's just not possible to completely eliminate unwanted sound & that's okay.  It's a natural part of playing guitar.

I cover muting techniques for beginners in the first few lessons of this tutorial.

https://www.guitartricks.com/tutorial/2281/

Hope that helps!