The opponent's Wedding Ring's second ability triggers, causing them to draw a card.
Notion Thief causes that opponent to skip that draw, and causes you to draw a card instead.
Repeat from step 2 until you remove a combo piece from the board at instant speed; if you do not you will draw from an empty library and lose the game.
Notes
The most straightforward use of this combo is in decks that have a way to win the game at instant speed after drawing their deck, for example by putting any Laboratory Maniac effect onto the battlefield at instant speed. This usually requires additional starting mana.