It's pretty hard with most games, as they use a codec of some kind, but you can extract the rom using DSBuff (http://gbatemp.net/index.php?download=1143) and then explore the files from there. Pokemon Diamond uses .mp3's, which makes it easy.

 

It is covered in a few other threads but DS roms have a file system and I have yet to encounter one that does not use it (granted some have stuff on top of it). Here you use ndstool (or frontends DSLazy and DSBuff, see the rom ripping link in my signature for this), ndsts, nitroexplorer or rip them from the rom with a hex editor.

In there there will be sound files.
The most common format (about 10 do not use it) is the nitroSDK sound format more commonly known as the SDAT format.
Details here:
Specs:
http://loveemu.yh.land.to/page/NDS/SDAT.html
http://kiwi.ds.googlepages.com/sdat.html

Once you have the SDAT file then:
Preferred tool for ripping: ndsdnsext
http://nintendon.s6.xrea.com/
Second link down on the left or ??????

You can edit the files and there is a rudimentary repacker available at the tahaxan fourms but by hand is best.

In stuff like electroplankton there are wave files which hundreds of things support.

Others use less common formats like AHX/ADX and things seen in other consoles.
A recent effort with the world ends with you (I had a link to a Japanese site that was really good for this format but I am on someone elses machine right now so I am afraid you will have to search for a little while):
http://gbatemp.net/index.php?showtopic=86998


Also see:
http://gbatemp.net/index.php?showtopic=33647
and crystaltile2 has rudimentary sound support.