Begin a Golden Age.
Golden ages are triggered by excess happiness. Each turn, the happiness total is added to your golden age counter. Once this counter is full, a golden age will unlock. Unhappiness will decrease the counter, until it reaches 0. So to trigger a golden age, you need to make sure your people are very happy.
You can also trigger a golden age with certain social policies, wonders, and great people. In the base game, any great person can start a golden age. In Gods and Kings, only Great Artists can start them.