The bit that connects to the 'phone line is called a router - (many, most all?) wireless routers are also capable of having ethernet cables connecting household computers - RJ45.
My old wireless router has four Ethernet ports which we don't bother using (but we could) - we typically have three or four machines using the internet wirelessly through the router and have had up to six at once.
Each connecting machine needs to have wireless capability or an RJ45 Ethernet Port and a cable.
Laptops typically come with a wireless card built in - desktops perhaps not - x-box I don't know (read the literature) Can you connect x-box via a computer or does it need it's own direct connection? Do these things have wireless capability or an ethernet port?
The Router is permanently connected to the Internet and local computers automatically "find" the router as they're switched on.
You do not mention the style of your Broadband connection
Peccavi
November 2009