1. Buy a wireless broadband router with its own inbuilt modem.
2. Equip each computer with a wireless network adapter - PCI cards for the desktops and perhaps a USB or PCMCIA card type for the laptop. If you don't fancy opening up the desktop cases you can get USB type adapters for them.
3. Set up all the hardware - plug the router into your BT phone socket - and make sure that you install any USB device software BEFORE you connect the device. There'll be a lead with the router that you use to temporarily connect it to one of the computers (it doesn't matter which one) so you can configure it (the router) with your username and password for your broadband ISP. Once you've done that you can disconnect the lead - the router will automatically make the connection each time you boot it.
If you're using Windows XP you'll find that each of the computers will connect to the router when you boot them, although depending on which hardware you buy you may be asked to choose the wireless connection to use - there'll only be one, unless someone who lives nearby also has a wireless network, in which case you might see that as well.
That's about it - the hardware installation should be very straightforward, and these modern devices usually configure themselves to a large degree.
Come back here if you're stuck.
Hardware? I usually use Netgear routers and PCI cards, or Belkin PCMCIA cards for laptops. You can mix and match - you don't have to stick to one make throughout.