How can I create a simple chat system for my multiplayer game?

I have created a small multiplayer game. I would like to know how to add a chat system to the game. Basically, I need a small textbox that allows the player to type his or her message, and a larger box that displays all of the messages. For now (since I don't have an online database for players to actually create an account), players would just enter their name each time the game starts, and that would be the name that is displayed in the chat.

I would think there would be a simple way to do this. All I need is some textareas, a large box for displaying the messages, and a method for updating the chat box to ALL players when a new message is added to the list.

I am trying to avoid all of the 30-60 minute tutorials out there, because they are all specific for their games, and I don't think it's really that complicated. (For example, other developers have created different scripts that are referenced in the chat script, so unless I've been following along with ALL of their tutorials, I will not have the correct scripts.)