Think of your DS as a Wifi device.
In order for it to connect to Wifi hotspots, you need to configure it to connect.
NOTE: Games that use the Nintendo WiFi Connection will allow you to enter this special menu from within the game. Look for a game that has the "Nintendo WIFI Connection" logo. All of these games allow you to enter a special WiFi Setting that's inside your DS/DSLite/DSi/3DS. You cannot see this setting without these games if you're using a NintendoDS or DSLite. I 'think' DSi systems allow you to see it from their homescreen without a game. The 3DS also lets you configure it without a game.
WHILE NEAR A WIFI HOTSPOT:
1. Turn on your DS.
2. Once you're at the "Warning - Health and Safety", touch the screen.
3. There are a few buttons on the screen. Touch the one for your NintendoWFC-Capable game.
4. Within that game, 'somewhere' there will be a "Configure Nintendo WiFi Connection" button (usually along its main menu). Click that.
Once you're there, follow the instructions on this website (why bother typing all of that up when it's all here):
**Clicky**Your DS allows you to save three different WiFi connections. When you're near a hotspot, its Wifi menu will scan and find the hotspot and show you what kind of connection it has based on the colored lock next to the connection (gray: incompatible connection, blue: open connection, red: WEP-password-protected connection). Try to find a connection that is blue. Those are usually open. You can also configure a Nintendo WiFi USB Adapter connection in this fashion. Your settings for connecting to the Internet are saved even if you use another gamecart.