Upon leaving the Gym, Drayden will walk outside and then tell you to follow him over to his house. Remember where that is? Yeah, it's the building in the middle of town, over by the Pokemon Center. You'll see him outside of his house anyway, so he shouldn't be too tough to track down. Make sure you heal up your Pokemon first, though!
Inside his house, he'll tell you about the Dragon-type Pokemon Reshiram and Zekrom, but will then tell you about a third one, Kyurem. After some talking, you'll be interrupted by the sound of something rumbling. It's not your stomach, no, it's coming from outside!
Outside, you'll see the huge Plasma Frigate from earlier, except it's FLYING and then suddenly fires ICE CANNONS at you! Whoa! No joke! Every shot freezes a part of Opelucid City, frosting it up pretty good.
Drayden doesn't appreciate that and sends out his Haxorus to try smash the ice, but it fails to work. Shortly afterwards, Zinzolin and two Plasma goons show up and talk a bit about N. They say some stuff and then leave. Drayden then instructs you to explore Opelucid City and track down any of the Team Plasma Grunts around.
Well, better get to work, and hope you like sliding. You can slide out of the ice near Drayden's house by sliding to the right and then down. Over there, you'll find Drayden taking on two Team Plasma Grunts. Ignore the one to the south, then take the one on to the east of the Pokemon Center. He has a Watchog L44 and a Muk L44.
After beating him, slide to the north until you reach the end, then a little west. You'll find another Team Plasma Grunt over by the door to a building. She uses a Golbat L44 and a Garbodor L44. Now go over to the west and then south to find yet another Team Plasma Grunt, this one with a Seviper L44 and a Weezing L44 on his team.
Once you've taken all three out, go back to the Gym in the northwest part of town and get ready to take on Zinzolin!
He's got some frosty Pokemon, but they're also at pretty high levels, too. His Weavile is particularly fast and hits hard, so watch out for it!
After beating him, he'll run off, and then Drayden will appear by you instead. He'll heal up your Pokemon and then briefly walk inside the Gym, giving you a special key item, the DNA Splicers, which he's held onto for awhile and tells you not to lose.
As luck would have it, though, one of the Shadow Triad appears, steals your new item, and talks for a bit before his two buddies show up and then run around through town. Oh man! Looks like there's more Team Plasma hunting for you in store!
Head on south and then all the way to the east to find one of the members Shadow Triad.
His Pokemon are all Dark-type, so Fighting-type attacks are your best bet, since the Pawniard are also part Steel-type.
After beating him, he'll teleport away with the DNA Splicers, leaving Drayden to run over and see if you're alright. Just then, you'll receive a call on the Xtransceiver. It's from Hugh and Cheren! They're basically, like, what just happened in Opelucid City?! And it turns out Cheren is nearby and telling you that there was a flying ship spotted near Humilau City. Drayden seems to think you can get there through Undella Town, so after wishing you luck in stopping Team Plasma, he leaves you free to head on over there!
At this point, several routes and areas will have been hit by ice, meaning you may need to slide around and find another way through than the usual way. However you go about it, make your way back to Undella Town!