Careful practice is the key to getting the hang of chords and chord changes.

Pay close attention to the angle of your fingers, especially from the tips to the first knuckle, as this is one of the main causes of muted adjacent strings (but, as you progress, you will start to learn techniques where strings are deliberately muted).

Pressing too hard on the strings is another common cause of "fat finger" problems, as this causes the fingertips to spread outwards (it also slows your movements and makes playing physically tiring).