Stay calm. Do not run away. Do not argue, resist, or fight the officer, even if you think the officer is wrong. Keep your hands where the officer can see them. Do not lie or give the officer fake documents…
You have the right to stay silent. If you want to use that right, say so out loud: "I choose to stay silent." In NH, you have to show ID if you are stopped while driving. If you are just walking, you do not have to answer questions or show your ID to police or ICE agents.
Regardless of your immigration status, if you are arrested by police, you have a right to a government-appointed laywer - if the offense can lead to jail time.