웃다 is a verb = to laugh 웃기다 is the causative verb of 웃다 = to make someone laugh So you can use them appropriately depending on the situation.

웃다=laugh 웃기다, 재미있다=funny, fun 당신 재밌는 사람이네요. You're funny. 저 시트콤이 웃겨서 웃었어요. I laughed cause that sitcom is funny. 파티가 정말 재미있네요. This party is a lot of fun. And 웃기다 is more appropriate for thing or situation. You shoud be careful to use 웃기다 to describe someone. For example, you're expected to say 당신은 재밌는 사람이에요 when you first met someone. 당신은 웃기는 사람이에요. may seem rude cause it can be used sarcastically.