I think what you are alluding to is a wireless router. Most electronic box stores carry them, there are numerous manufacturers so they are easy to come by. They are often times used in conjunction with another device, a modem and there are a couple of different types, cable and dsl, the modem links to the router via an ethernet cable (looks like a fat phone line) and you are in business. There is another device that is quite commonly used by (sometimes provided by) internet service providers and that device is called a "GATEWAY" basically it is a modem/router combination unit and can be either cable or dsl, depending on the server. Next time you are in an Office Depot or Staples, take a look in the tech department and you can see what these items are for yoursel. Good luck!
I can not for the life of me think of what you call the part that connects new computers to your home wi-fi network (i.e. the part you need so you can have more than one computer on your network).
I know it sounds silly but it is one of those deals where something is on the tip of your tongue but you can't think of the word. When you are done laughing, please help.