Wow, you could provide more information, if you'd like, but since guessing is our hobby, I start with
System Preferences > Sharing > Internet Sharing, then choose the adapter from which you get the internet and select AirPort (wireless) as the new sender (To Computers using).
So if you get internet by ethernet cable you can broadcast that via AirPort and your DS Lite can connect to it, if it is even capable of doing so. The other way around is less likely, as the DS Lite may have NO Ethernet port.
Or try it via USB. Or Firewire.
Seriously, what kind of network setup do you have and what hardware and software settings are involved?