You'll need -
1 - a broadband connection with Ethernet
2 - a WiFi access point/router
3 - a wireless network adapter for each PC, laptop or device on the network
Firstly, you need to check what kind of modem you have. You'll need an Ethernet modem, not a USB modem. Some ADSL ISPs provide an Ethernet modem, but most don't.
A Cable modem or set-top box (NTL, Telewest, Blueyonder) always has an Ethernet port, so it can accept a WiFi router.
If you have an ADSL USB modem - you'll need to get an Ethernet modem, like this one
Once your modem is sorted out, you need a wireless router/access point to broadcast the connection wirelessly. You can purchase a combined Wifi Access Point and Router such as
A wireless router always has a few ports that you can plug wired computers and devices into also. It's generally a good idea to set it up and configure it with an Ethernet cable first.
The scenario above shows a DSL modem, but the same principal works for ADSL and cable - the Ethernet connection from the modem or set-top box connects into the Internet (or WAN) port on the router.
When your wireless router is working properly with your modem and computer, then you'll need to get a wireless network adaptor for each PC, laptop or device. See this guide
for advice on getting the right network adaptor.
If you're an ADSL user with a USB modem - you can alternatively get a WiFi router with an ADSL modem built-in. This is the most convenient solution for those with USB ADSL modems, as it can replace your ISP-supplied USB modem and give your home network WiFi functionality all in one box.
Digidave recommends for ADSL users the 2WIRE Home Portal 2700HG Wireless ADSL Modem/Router - 2WIRE Home Portal 2700HG