There are two different types of surveillance:
surveillance that doesn’t require any special power to carry out because it is within the normal scope of a citizen’s rights and powers, and
surveillance that requires special permission (like a court warrant) because otherwise it’s against the law.
Anyone can carry out the first kind of surveillance. We can follow someone to see where they go or find out where they live, we can observe who they visit or we can listen in when someone on the bus is talking on their phone. So long as we don’t interfere with someone’s rights (for example, their right to privacy) or otherwise break the law, those actions would be legal.