First off, just as a tip, it's always good to mention the name of the game, whether you're requesting or just asking for help. It just gives us an idea of what we're working with, like maybe someone knows a super simple way of ripping from this particular game. After a quick Google though I found that it's Golden Sun: Dark Dawn, so no worries.
Now, there are 2 common ways you could try ripping this; extracting the images from the ROM directly, or hard-ripping.
The first option is usually the ideal way of doing it, since you'll get clean rips as they're stored in the game. For DS games the most used program is Tinke. Look around in the file structure, you might find some formats it recognises that you can extract. If not, you can try Googling or asking around for information on the files you do find.
The other way is hard ripping. This includes playing the game in an emulator until the graphics appear on-screen, taking a screenshot, and removing the unnecessary stuff. Of course this is incredibly difficult (and often impossible when stuff is on top of each other) unless you have an emulator that can disable layers. The most popular one for this is DeSmuME. If you disable all layers except for the one with your sprites, you should hopefully be able to take a screenshot from which you can easily obtain your sprite. It does depend though, some games use layers in an inconvenient way.
The first case is usually something you'd try first, hard-ripping is often used as a last resort, or if it's easier to do it that way. Sometimes it's just too tedious or nigh impossible to do though (especially when trying to rip character sprites with lots of effects or something). In that case there are some more advanced methods you can try if you're determined enough (tile ripping, trying to convert/extract unknown formats, etc). With luck that shouldn't be necessary in this case.
Hopefully that should get you started. Feel free to ask if you need any help
Now, there are 2 common ways you could try ripping this; extracting the images from the ROM directly, or hard-ripping.
The first option is usually the ideal way of doing it, since you'll get clean rips as they're stored in the game. For DS games the most used program is Tinke. Look around in the file structure, you might find some formats it recognises that you can extract. If not, you can try Googling or asking around for information on the files you do find.
The other way is hard ripping. This includes playing the game in an emulator until the graphics appear on-screen, taking a screenshot, and removing the unnecessary stuff. Of course this is incredibly difficult (and often impossible when stuff is on top of each other) unless you have an emulator that can disable layers. The most popular one for this is DeSmuME. If you disable all layers except for the one with your sprites, you should hopefully be able to take a screenshot from which you can easily obtain your sprite. It does depend though, some games use layers in an inconvenient way.
The first case is usually something you'd try first, hard-ripping is often used as a last resort, or if it's easier to do it that way. Sometimes it's just too tedious or nigh impossible to do though (especially when trying to rip character sprites with lots of effects or something). In that case there are some more advanced methods you can try if you're determined enough (tile ripping, trying to convert/extract unknown formats, etc). With luck that shouldn't be necessary in this case.
Hopefully that should get you started. Feel free to ask if you need any help