Nintendo have released a patch for Mario Kart 3DS, the first game on the handheld to receive any post-release fixes. There's nothing too meaty in there – you shouldn't expect new characters or extended single player – but it does fix some fairly serious glitches in the game's multiplayer, a big issue that allowed users to skip over half of some courses using exploits in the level design.
You won't be able to play the game online until you've downloaded the patch and it won't be done automatically. You'll need to jump onto the 3DS store to access to patch, titled "Mario Kart Update Ver.1.1," and you'll download it from there. Simply download and the patch will be applied, allowing you renewed access to the game's online mode and a new chance to win matches on something of a fairer footing.
It would be nice to think that a future system update would make this process a little less involved, but I'm sure Nintendo will be looking into download figures and the like and will make a decision from there.