If you do not like the idea of using the command line interface as suggested above, you can use System Information to get the same information.
Click the Start button -> All Programs -> Accessories -> System Tools -> System Information (from my W7 box, Vista and XP are similar) to open the System Information dialog box. Expand the Componets tree, then the Networks tree and select the Adaptor branch. Scroll down until you find the information for your network connection, it will contain information as described above.
The gateway is probably your router, I say probably because in my case it isn't (thanks Telstra for a next G modem that doesn't connect to a network, I have to use a couple of other smaoke and mirror boxes to use my Internet with a network). Then you can use a browser to connect to the router. If the password etc has been set but forgotten you can reset the router to factory settings by pushing the end of a paperclip into the reset button. If you do thois you will lose all your settings so use it as a last resort and only if you are happy reconfiguring a router!
To set up your laptop/ notebook to access the wireless network depends on the operating system. Vista and W7 will detect a wireless network and offer to connect using a popup at the lower right corner.
If that doesn't work open the network and sharing center (W& Start -> Control Panel -> Network and Sharing Center). Click the Connect to a Network link.
HTH

