It is currently unknown what level you have to be in order to get Master Balls as they have not been added to the game yet. They are going to be added to a future update. Right now, they are inside of the code of the game, though, and they have a 100% catch rate.
If you have not unlocked Ultra Balls yet, then be sure to use Razz Berries in conjunction with Great Balls for an extra effect. If you have not unlocked a Master Ball but you have potentially come across a Legendary Pokémon or something of the ilk, use Ultra Balls in conjunction with the Razz Berries to make the Pokémon in question easier to catch.
The best place to find all of these balls is an area with a lot of Pokéstops. Areas with the most Pokéstops include downtown areas, old-town or historic districts of cities, or other areas of note, such as a Chinatown or other historic ethnic enclave. Church districts are also good. Any area with a lot of memorials and murals works, as well. Just stay out of cemetaries as even though they tend to be loaded with Pokéstops, it is also important to show respect.
Make the most of your Great Balls, Ultra Balls and Master Balls by saving them only until you really need them. Great Balls, if you have a limited number, should only be used to catch rare Pokemon that you can’t get with a great/nice shot, mixed with a Razz Berry, mixed with a Poké Ball. Ultra Balls should only be used to catch extremely rare Pokémon with a ton of CP that even Great Balls and Razz Berries won’t work for. As for the Master Balls … save those for the legendaries because both are expected to be added to the game at the same time.
Look for special events to be hosted by Nintendo and Niantic. These events will provide you with extra chances to earn big rewards, including but not limited to Master Balls.
As the game gets older, too, expect future updates to add Great Balls, Ultra Balls and Master Balls to the in-game store, potentially, allowing you to buy them with Pokécoins. Until then, and if you run out of the Great Balls, use Razz Berries (and the future berry unlocks) to make tougher Pokemon easier to catch with a lower-tier Poké Ball. Razz Berries can be earned at Pokéstops everywhere.
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