If you just bought an HP notebook it should have the minipci card built in (it should be referrred to likely as an Intel 2100 if it is B wireless only (original standard) or Intel 2200 b/g if it is the newer standard (supports b and g which is up to 5x faster). Or, you may have a Broadcomm minipci card.
You should have a button somewhere on your notebook (a blue light and the button is on the front of my HPZT3000/Compaq X1000 series) that you push to indicate you want the wi-fi activated on your notebook.
You only need a PCcard or USB wi-fi device if you didn't have the built in wi-fi (all desktops and older notebooks).
All you need is the router and any decent brand should be compatible. Once you set up the router (if you have a b/g minipci card you should get at least a 54G router which is backwards compatible to B) -- Dlink, Linksys, etc should all be fine -- you need to set up encryption to keep your wi-fi from being used by everyone ...
then, you have to go into the notebook and put in the encryption code -- once set up you don't have to worry about it -- if you turn on the wi-fi button it should instantly be logged onto your DSL or cable modem whereever it is in the house.
The internal wi-fi card keeps you from having to keep sticking in the external card and it is more efficient as well. Make sure you turn off the wi-fi button when not using wi-fi as that will save your battery life or even electricity (A/C) when not in use.
At my home I have a desktop HP Pavillion,I have cable internet on it & I'm the only one who uses it. I recently bought a wireless notebook (HP pavillion) so as to do some lessons while traveling. I know I might need a router, but do I also need a PC card too, one like this?:
Linksys Instant Wireless Network PC Card, WPC11-Version 4

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic