Enterprise is rushing to a mining colony disaster to render medical assistance, but then Q stops them with his crappy forcefield. Q appears as a floating glowy glass ball with three snakes on the top, with shiny lights orbiting it. Oh, it's an Alderbaran serpent.
Q attempts to banter and insult Worf, but Picard bitches him out for the earlier events of Encounter at Farpoint. Q responds by removing the rest of the bridge crew to some alien world or other, leaving Picard alone and trapped on the Enterprise bridge.
Riker sits down with Q and has a drink of lemonade. God, this is slow moving. Q explains they're going to play a game for some reason or other, and beams Yar to a penalty box, explaining that if anyone else incurs a penalty, they'll be zapped to same box and Yar will disappear into oblivion.
Back on the Enterprise, Picard wanders around a bit. And wanders around a bit more. And tries to make a log entry. Then Yar appears and provides some exposition, then bawls a bit until Picard comforts her a bit, and Yar says she would so do him if he wasn't captain. Then Q appears, says the penalty is over and makes a Captain's Log of exposition. Picard makes a wager about whether Riker will win the game or not.
On the planet, the others watch Worf do some reconnoitering.
Meanwhile, Q is quoting Shakespeare. And Picard totally pwns him with quotes, so he storms off in disgust.
Riker checks the phasers still work, and Worf immediately appears. "OMG! A fight! Where?!" Q tells Riker he now has the power of the Q and can transport everyone back to the ship, so he does.
The Enterprise, meanwhile, is back on course when the bridge crew sans Riker reappears. They discuss Riker's fate, but proceed on course.
Riker has a wee laugh and then talks to Q a bit. Q explains about the Q continuum and how humans are Special, so they've selected Riker to become a Q so he can help them understand humans. Q disappears, returning the bridge crew including Picard and Wesley to the planet. The enemy soldiers turn up again and Worf attacks them, but is stabbed. Then Wesley runs over and is also stabbed. Alas, the two most annoying characters on the show don't remain dead long, as Riker uses his 1337 Q power to bring them back to life and return everyone to the Enterprise. Whereupon Picard is all "Double-you Tee Eff, bitch?"
Riker is now... DEUS EX MACHINA MAN!
Picard gives him a speech and says he has to refuse to use the power. They reach the planet where the mining disaster occurred and Riker's team beams down to take a look. There's a bunch of injured miners, and a dead girl they find under the rubble. Data suggests that Riker could, you know, bring her back to life, nudge nudge wink wink, but he says he promised Picard not to. Then he goes back to the Enterprise and glares at Picard a while.
So, later on, they decide to have a discussion about Riker's new powers. Talk talk talk. Come on, blow something up already! Q turns up dressed as a monk to lend Riker moral support. He suggests Riker give his fellow crewmates gifts, and Picard authorises it because he's clever and knows that it's all going to go HORRIBLY WRONG!
Riker starts by making Wesley ten years older, and a male model. Data refuses the gift of becoming human, but Riker gives Geordi real eyes. Geordi is happy for a bit, but asks Riker to change him back. Riker does so, then makes a female Klingon for Worf. Will T Riker, intergalactic pimp! Worf says he has no place for sex(!), and then Wesley asks to be changed back. Finally Riker realises he's been an idiot. The other Q yank Q away and return everything to the same place as before. Teh end.