How does matchmaking work in Play mode?

Solution 1:

From http://hearthstone.gamepedia.com/Play_mode:

Casual

Matchmaking in Casual mode is determined by matchmaking rating, aiming to match the player against an opponent of comparable skill, with wins and losses affecting future opponent selection.

Ranked

There are 25 regular ranks, and an extra rank, 'Legend' above that. Each rank has its own medal and title, with ranks 2-25 named after minions from the game. All players start at rank 25: Angry Chicken. Players of ranks 1-25 will be matched in battle against players of similar rank, while players of Legend rank will be matched against other players of Legend rank, according to their matchmaking rating. Note that ranks are numbered in diminishing order: the smaller the number, the higher the rank.