In game chat is where you can find yourself a guild to join, to invite new members to your own guild or find someone to exchange Improvements points with to upgrade your shop. (offcourse, chit chat about the weather, your new love, or whatever else can be done there too ;) )
Type your message in the field at the bottom of the chat window and click Submit or press Enter on your keyboard. This message will be visible to everyone in the chat.
To whisper double-click the name of the person in the name list on the right side of the chat window or type /whisper "Person_name" before your message in the message field.
Beside the ingame chat, on sites like Kongregate there is also the chat channels available for this specific site.