When an update is available for any given selected game, a notice will appear at the bottom of the screen informing you of the available update. Upon launching the game a dialog box will appear again informing you “A software update is available.” You can skip this update by launching the game using the “(A)” button.
However, if you press the “(Y)” button, a new “Software Update” dialog window will appear. Selecting “Download Now” prompts another dialog window informing you “This process might take some time to complete.”
If you’ve never used the eShop Selecting “(A)” to continue results in a sort of Terms of Service agreement being displayed. (To Exit this menu, press the power button, then the home button). After pressing “OK” to accept the agreement you’ll be prompted to Sign in to the Nintendo Network. I don’t want to sign in, so I’m going to update the game using another simple method.
You can use FBI to scan QR codes that will update games, these updates can be found on a certain 3DS Title Key site (Google is your friend) by searching for the game name, followed by “updates”, example: Hyrule Update.