In addition to what anares said:
You contact human and AI civs the same way as you do in Civ3.
Trading with AI civs looks exactly like it does in Civ3.
There's a text box for chatting, and the output is displayed in the upper left corner of the screen (where all messages (chat, civil disorder, completed build orders, ...) are displayed).
There are three radio buttons that allow you to appear happy, neutral, or angry.
You can always chat in a game, and can block chats (outgoing, and I think incoming). My friends and I often use this as a way to say stuff that we don't want others to hear like, "I need to contact you in a few turns. Our lux trade is going to expire."
When a human civ wants to start diplomacy with you, and can accept the envoy, reject it, or reject it for the next 20 turns.
There are times when the human civ is in contact with another civ. On the diplomacy screen (f4), you'll get a message when you click on that leader that's already in discussions. It says something like, "So and so is in discussions with someone else. Perhaps you should try back later."