Verizon is providing in-home internet access? The only way I know of this happening would either be a mobile broadband card or a MiFi mobile hotspot.
If he has a laptop with a wireless card (they don't make laptops without them) and a router (whether it be cable/phone line based or a mobile broadband thing), that is all you need. You have to pay for the service coming to the router, the router sends the signal out, and the laptop uses it to connect to the internet. It's as simple as that really.
As for setting it up, he will have to follow the directions given in the manual that comes with it.
Your setup is different because you are likely using a regular line-based internet connection (cable in the ground), where what he will have (according to my guess about what you said) a completely wireless setup (wireless from the provider to the router and from the router to the laptop). There isn't anything else he needs to buy. Unless he wants a wireless printer, that is.
If all he is doing is buying a regular line-based router from Verizon, there is no point in doing that. Verizon does not offer line-based in-home internet, so they would just be charging him extra for a router (that Verizon cannot send service to) that you can get at Wal-Mart. And in that case, he would have to find service through a company like AT&T, Charter, etc..(ones that offer in-home internet).
Edited by keyboardNinja, 28 January 2010 - 09:46 PM.