The first chapter is about learning. In Chinese learn is 學. However, learning usually is referred to as 學問. The second word 問 is "ask". So to Chinese, learning consists of "learn" and "ask".
子 refers to Confucius. Strictly, it means "master". 子曰 is "master said".
學而時習之，不亦說乎? as translated directly is "to learn and revise often, is it not a joy?" The question is learn what. If it were knowledge, revising a piece of text often isn't much joy, right? As I have pointed out, to Confucius, 學問 is not about career path nor knowledge. It is about one's character (attitude and behaviour) and potential - when translated into modern concepts. As one builds up a character (學) and keep on practicing such attitude and behaviour is definitely a joy. Here the modern meaning of 說 is "say". But in Confucius days, it was equivalent to 悅 which means "joy".
有朋自遠方來，不亦樂乎? When a friend comes from far away, is it not happiness? Again, the meaning really becomes clear when we understand that "朋 friend" means someone who share the same character and attributes. When someone who possesses good character is visiting, the chance of learning from this person is the source of happiness.
人不知而不慍，不亦君子乎? This sentence contains 不 three times. 不 means "not". People does not know and you do not feel angry, is it not gentleman? Does not know what? Again, Confucius was emphasizing if people does not know or understand his teaching - his philosophy - that's not a cause of wrath nor anger.