You gain Stamina automatically over time. In addition, at noon (12:00) and 6:00 PM (18:00) server time, you will receive a quest reward granting a bit of Stamina. If you do not claim these rewards prior to 5:00 AM the next morning, they are lost forever!
Finally, you can purchase Stamina using Diamonds either directly by clicking on the green + next to your Stamina counter in the upper right part of the main screen.
You will consume an amount of Stamina for each Adventure stage or Hero Chronicles page you complete. In return, you will gain the same amount of League Level XP. Since League Level sets the limit for how much you can level up your Heroes and Angels and also unlocks higher tiers of content, it is a very important area to focus on.
Spending Diamonds on Stamina will be one of the wisest investments you can make. Being able to level up your League quickly (and therefore unlocking the ability to raise your Angels and Heroes and other perks) will make the most difference to your power level in the game. Even as a Free to Play player, you will accumulate Diamonds to use for this purpose.
Some people like to show off how they have stockpiled Stamina. However in the long run because of the accumulation over time (which stops when you're over your max Stamina limit), and now the limited ability to purchase more when you are over another threshold, that is not as useful as Adventuring / Blitzing as much as possible to gain XP for your League and Equipment/Gold/EXP Potions for your Heroes and Angels.
While you are still leveling up and acquiring Heroes and Gear, pay attention to the special "x2 Drop Rates" Events. For Normal Stages, that will be on Mondays. For Elite Stages, the Double Drop-Rate Event occurs on Tuesdays.