I'll cover through the explanation if you don't want to purchase the Nintendo Wi-Fi USB device.

What you have to do in order to connect is to be in range of a wireless router. Before accessing the Wi-Fi option(s) within the game, you have to setup your connection. The tools to do so can be available right on the multiplayer screen, or in the Options menu. You can set up to three different connections, which can be handy if you play with your DS in a few different areas. The system attempts to detect any router in range. Just select whatever router appears to have the strongest connection, or one that suits you the best.

If the wireless router is secured, you need it's access key (such as a WEP key, for example). Also, if it's the kind of connection that, on a laptop, requires you to login on some webpage in order to access websites (my University does this), it won't work.

Any game that has Wi-Fi support comes with an extra manual describing how to connect. It will probably clear up any point that I might have overlooked.

What you probably mean is the AOSS setting. Some brands of routers have a mode to allow supported systems to connect easily. You don't need it, though: I don't have it myself.

The range of the wireless router depends of the router itself, along with the walls of the house and several other things. For example, a cordless phone can cause interferences, forcing you to stand closer to the source. In my case, I can easily connect from anywhere within the house.