When you give someone a good, long look, you regard them. It can also mean "to believe," as in "I regard her as my best friend."
Regard often means respect and admiration, as in "I have the greatest regard for my grandmother." Sometimes it's a greeting: you can send someone your regards, which means to tell them you said hello and wish them well. There's a famous song called, "Give My Regards to Broadway." On the other hand, you can use it as a sign-off on a letter. Instead of "Sincerely" or "Yours Truly," you can close with "Regards."