There is some homebrew that communicates over standard TCP-IP and thus can be used.
Similarly I am sure you could run a self contained version of the save ds wifi stuff on your own network and use that, or indeed you could probably use a remote hosted one that already exists and try to get them to meet on that if you are happy to have an internet connection involved in this. For the self hosted thing I have no guides I can point to but running the server program, hacking the games and fiddling with a DNS server to allow it all is nothing too drastic. For the internet thing then whatever you need to run a game on that will do here as well.
As far as conventional local play and "download play", which is what I find most people mean when they ask this sort of question, then probably not very easily -- the DS uses a fairly custom protocol (most call it nifi) that most network cards have trouble with (and similarly there are no "buy this specific card, install this specific driver" type things I can link you to like I can for some other aspects of hacking consoles or networks). I imagine it is quite physically possible* but you would be building it all from the ground on up to do it.
*three main scenarios
1) You gut a DS (find the classic scratched screen pink DS with knackered battery) for its wifi components, or install something and some DS homebrew that captures the packets and sends them onto a PC for use with the emulator.
2) You get one of those really nice software defined radio** wifi cards and reprogram it to speak the DS wifi language, also make drivers for that machine.
3) You get some fairly expensive radio electronics/physics gear with a nice USB/network/whatever capture and send function, send it to your PC and also build a radio to reply to the DS. Most of the gear is at enthusiast level these days but still not easy money.
None of those is easy, however none of those (save perhaps finding a card for 2) as I have not looked in a while for such things) is beyond a fairly skilled electronics person.
**if you go through network/wifi hacking circles you will find all sorts of things dealing with raw sockets, some NDIS level stuff, straight custom drivers and so forth. They are useful for various types of network attack and make certain things easier, also the ability to use them is blocked by various levels of software (modern non serverWindows being some of the most restrictive there is). Software defined radio is a level above this still, and some countries get a bit touchy about people having them.
