You are the smartest person I know. Comparitives and superlatives are used to describe differences between two or more nouns. Example: Jim is tall. Bob is tall. Bob is taller than Jim. Here we use (adjective + er and the word "than") If we add another person. Ted is tall. Bob is taller than Jim. Ted is taller than Bob. We can say Ted is the tallest. Here we use the word "the" + (adjective + est)

first one is correct!

"You are the smartest person I know" is correct. "You are the smarter person I know" sounds like you're talking about someone who did something stupid.