To get wireless access to internet with laptop, do I just need a wireless router?

Nope - just a router will do fine.

probably don't need anything else. older laptops didn't have built in wireless capability so you would have had to get a wireless card for it to work. Laptops built in the past several years have a wireless card built right in. You just have to configure the SSID on your router to be a secure connection, then setup your laptop setting to match the router. .. not a big deal. you will be up and running in no time. Just give a call to the router tech support line and they will take your through it.

You are correct and ALL you need is a router. Most DSL providers (i.e. AT&T) these days will actually offer EITHER the DSL modem alone, or a DSL Gateway. Basically the Gateway is just a DSL modem and a Wireless Router (and usually 4 ports of LAN switch) in one box.

Since you have the DSL modem up and running now, and it is attached to your desktop with a LAN cable, you can simply insert a Wireless Router into the path. Modem cabled to Router on "WAN" port, then router cabled to desktop using one of the 4 "LAN" ports.

You can find wireless routers of this type for anywhere from Free-after Rebate, to $100 or so. I like the Linksys Wireless G router which is commonly sold for about $39.99. Any quality wireless router will do. Make sure to choose one that has 4 ports of LAN on it as well.

Once you have it working with your deskotp, you follow the router instruction manual to setup a wireless SSID (hotspot) in your house.

Choose something like MYNET, and try to find MYNET on your laptop. Avoid the urge to turn on enryption or anything else fancy UNTIL you have the laptop and desktop working per the above instructions...

(After the successful setup, you can venture into turning on WEP encryption and /or MAC filtering, etc)