Before starting a match, you will need to select a game mode:
  1. Tap Multiplayer on the main screen.
  2. Tap Match in the upper left corner.
  3. Tap the white box in the bottom right corner to open the game mode picklist.
  4. Select your desired game mode.
  5. Below the game mode, you can also select a specific map to play.
Once your game mode is selected, you can tap the buttons in the lower left corner to manage your Scorestreaks and Loadout, or you can tap Start in the lower right corner to begin the match.

You can also use the Invite Friends menu in the upper right corner to invite other players from your Friend List.