The two free ones are Flipnote and the DSi browser. If you've already got those, then the rest need to be paid for - just like games in a store.
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My son's DSi did not have this and I downloaded for him from the free DSI Ware site. My daughter's DSi, purchased on the same date in the same Target seems to have the FlipNotes pre-installed....strange....
if it is dsi ware yes
you buy them from a gaming store.
No, the DSi is only compatible with DSiWare.
Go to Nintendo DSi Shop. There will be games where you have to trade in DSi Points for the game and there are some that are free. Just click on the free game and click download.