You would need something like this. It’s called (this particular one) and R4 card. It allows you to install onto a micro SD card homebrew games, and ROMS of your games. ROMS are files that you can download off of the internet. I will NOT tell you how to get ROMS. It is illegal to download them unless you own the game. If you want to download them, Google it.
Because this functions with the micro SD cart, you can take that card and put it into a card reader on your PC or Mac. Then you can browse all of the files that were on there.
There are many places you can download .sav files, and you can download other formated saves as well (like .duc). If you are interested in learning exactly how these things work, get onto Youtube or Google and do a little searching. I’m more of a PSP modder, so I’ve never done anything with my own DS. I have many friends who do this with their DSs and I’ve been present for most of it. So that’s just what I’ve seen.
There are many forums that are on the web just waiting to help you, so if you are interested in learning more about how exactly to use the R4, then I’d try looking at those forums.