How do you change an animation while another animation is occuring?

Before you say something like, "You didn't even try," or something like that, please understand I've been trying for over an hour but cannot get it to work. What I'm trying to do is make it so that your animations (e.g. walking, idle, etc.) instantly change when you click the button to change them. What I tried basically kept breaking the animation, I tried disabling the script and changing the animation ids and re-enabling them.