I don't even have a VGC team ready. Is it possible for a

IIRC you have to play some matches, but you don't have to win to get the stones.

Just slap a team together and get in three battles. If you want to aim for a few wins try to look for some decent competitive mons

Forgive my stupid question but I've never bothered with any sort of Pokemon competition before so, uh, how do I sign up or whatever?

>>31638223
Sign up to Pokémon Global Link first.

https://www.pokemon-gl.com/

>>31638223
Registration period is 16th-23rd February
During that time, make sure your game is synced to the Pokemon Global Link website, and there'll be a link on there to sign up for the tournament.
After the tournament has started (February 24th-26th) you can pick the "Online competition" from the Festival Plaza Battle menu, which will link you up with people. You will have to put some Pokémon into a "Battle Box" in your PC (which, IIRC, you access by pressing X twice in the PC, it appears as if it's a second party). After starting the tournament, you won't be able to remove them from the battle box until the tournament is over.

The online tournaments aren't really very organised, they don't follow any single elimination, swiss, groups etc. tournament format, it's just about battling online repeatedly to stack points up.