GAH! NO YOU CANNOT USE A ROUTER.
All you need is a wireless card (PCI/PCMCIA, NOT USB!) with a RT2560 chipset. These are very cheap, from $15-$25 US and even cheaper in Europe.
You also need a special homebrew driver for the card. If you use the card to do DS demos, you cannot use it to do anything else. The driver is not compatible with normal wireless network protocols, only the DS protocol.
That said, it's dirt cheap, and there's a large collection of demos available now. The original E3 demos (especially the Submarine demo) are worth it alone. There's a very good tutorial on the forum, just search for DS demos.