Animator Controller Tutorials

Search for Unity's Locomotion tutorial. It's all handled in there.

Create an Animator Controller in your project hierarchy then open it in the Animator Window. Add your animations and create transitions. Click the transitions and add parameters to control the transitions. Control your parameters from a separate, single Animation script. You can handle the whole thing by switching a few booleans.

Make sure the correct animations are snapped-in to the states when you click them in the Animator window.