The answer depends a little on what sort of game you are updating, and where you want to be able to use it.
If it's a .3ds or .cia game that you've installed, then you can simply obtain and install the .cia containing the update. (You should be able to find them on the same sites you obtain your other files.)
If it's a retail game card, things get a little trickier. If you are on an Old 3DS, you can update your emuNand to the newest System Version. This will allow you to access the eShop and obtain the update normally. You can then use Classic Mode to run the retail card, and since your update will have a valid signature (coming from the eShop), it should work just fine.
If it's a retail game, and you are using a New 3DS, or an Old 3DS but you want to be able to run the game on sysNand, you will need to spoof the System Version for whichever nand you want to get the update installed to. I'm not too sure how to go about doing this for emuNand, but the guides should be able to give you more information on this.