Arcade games are free to play. Start SC2 and click "F5". You should see the start screen of the Arcade (registered trademark by Blizzard).
What is Arcade?
Arcade offers games like "Zealot Hockey", "Tower Defense", "Footmen" or "NexusWars".
Arcade offers the StarCraft community an exciting new way to discover, rate, and play a wide array of community and Blizzard created games. Arcade is available within the StarCraft II client, located in the main menu at the left of the screen after you log in.
If you want to create an Arcade game on your own, you should check out StarCraft II Editor.
Work in progress ...