Blizzard held back competitive play from Overwatch in order to give the base game its undivided attention prior to its May launch. Patch notes published on the game's official website reveal that a new patch available on the PC version's Public Test Region (PTR) contain the feature, as well as some general updates.
"Once you hit level 25, you’ll have access to our newest feature: Competitive Play," Blizzard explained in the patch notes. This mode was designed to be a more serious experience, allowing players to hone their skills and perfect their strategies. But before diving into the fray, you’ll need to play 10 placement matches. These will allow our matchmaking system to gather enough information about your abilities to assign a skill rating."
After attaining a skill rating, Overwatch will do its best to pit you against players at or around your skill level. As you win, the competition will become more fierce. If you lose, expect competition to become decidedly less so.
As its name suggests, anyone can participate in the game's PTR, though you'll need to run the PC version to jump in. Restart Battle.net, click the Overwatch tab on the menu located on the left side of the screen, select REGION/ACCOUNT, then click PTR: Overwatch from the drop-down menu.
PTR supports up to 10,000 players, so do your best to get in before the other 9,990,000 users catch wind of the patch.