Here's how to tell:
Action Verb: When "look" describes an action, it's an action verb.
* Example: "I look at the sunset." (The action is looking)
Linking Verb: When "look" connects the subject to a description of the subject, it's a linking verb.
* Example: "You look tired." (The linking verb "look" connects "you" to the description "tired")
Let me know if you'd like to see more examples!