There are several ways to acquire Dragon Points. The most common way is from defeating bosses-type monsters. After defeating them, the Envoy will acquire an amount of Dragon Points. This amount can be increased by using Azurian Stone of Divinity.
On the bottom of the interface, there is a bar that fills every time Envoys acquire Dragon Points. Once Envoys meet a certain amount, a reward will be sent to through the mail. This bar resets every month, so farm with caution.