Since Google is now handling all matchmaking, a G+ account is required if you want to create a game. If you are signed in with a G+ account, you can create a game, pick a room and choose a partner by going through:
Multiplayer->Invite Friends->Select your Location->Select your Level / Dungeon->Choose a friend or Auto-pick Player
If you choose auto-pick Player, this will create an open room with a random player. If a player is looking for the list of free rooms that was in the game previously, this is a feature that Google may be working on getting us.
To go into a random room, choose Quick Play in the Multiplayer menu. Please keep in mind, sometimes rooms will start and players will drop out before it loads completely.
Google+ is required because they will be handling all the cloud saves. When you save your game on the cloud it should not impact your gameplay. If you decide to switch between devices, be sure to save your game progress to the cloud. If you have two different versions of the game on your devices, you will be asked to choose with which game you'd like proceed. Keep in mind, if you make a purchase in a later level and then return to an earlier level where that purchase cannot be used, you will no longer have access to it.