If you have a modem for your broadband already that connects via ethernet (like chunky phone lines, with similar endings), then a router will suffice. This tends to be cable broadband, from the likes of NTL and telewest. ADSL broadband, that through your phone line, is usually set up with an USB modem. If this is the case, you'd be best getting a modem+router in one.
If you don't want a mass of cables, and your house isn't that huge, then you could get a wireless router. Then you'd just need some wireless dongles to plug into each of your kids' PCs, and they'd be able to access the internet wirelessly.
Something like this (ADSL modem+wireless router):
http://www.ebuyer.com/UK/product/52244
Then you'd need some adapters like these:
http://www.ebuyer.com/UK/product/60014
for each of your computers.
if you don't want to go down the wireless route (wired connects are more reliable, because wireless can have interference problems), then you could get something like this:
http://www.ebuyer.com/UK/product/52754
and some cables like these:
http://www.ebuyer.com/UK/product/106457
which is 15m long -- longer ones are available though. your local electrical store, like radioshack, will stock them. just look for cat5e or cat6 ethernet cables.
(note the prices of the wireless and wired routers that I link to -- probably best to just get wireless model anyway, even if you want cables. the wireless is exactly as the other model, but with wireless too.)