UI button trigger animation

First, open up your animator and create a new bool called "Run" or something you'll remember.

Next, write a script such as this, and place it on the character.

  public void PlayAnimation() {
     GetComponent<Animator>().SetBool("Run",true);
     }

Now, make a new UI button and click the "+" button to add a new OnClick function.

Next, drag your player into the GameObject prefab slot, click on the dropdown menu at the bottom, find your script's name, and go down to the function you made (For instance, it would be called PlayAnimation() in this case).