There are currently 4 know types of Poké Ball in Pokémon Go. These are Normal Poké Ball, Great Ball, Ultra Ball and of course the Master Ball.
The standard Poké Ball you get when you start the game. These are readily available at all Pokéstops and are great for catching all the entry-level critters that are lurking out there in the wild. You can catch most Pokémon upto 200 CP with these balls in the 1st or 2nd attempt. Any more than that and you're just having a bit of bad luck!
As well as finding these at the Pokéstops you can also purchase them in the online shop in exchange for Poké Coins. Currently 20 Poké Balls cost 100 Poké Coins, 100 Poké Balls cost 460 Poké Coins and 200 Poké Balls will set you back 800 Poké Coins.
These are the next step up from the normal Poké Balls and make it easier to catch Pokémon of higher levels. You will receive Great Ball's when you reach level 12. I tend to use these for Pokémon with a CP value of beteen 200 and 500. It may take 2 or 3 attempts but with patience and the help of a Razz Berry or two you can catch most of them in 2 or 3 attempts.
Now were talking! When you manage to get to level 20 you are rewarded with a bunch of Ultra Balls, they also become available to collect at all Pokéstops. Ultra Balls are great for catching the strong Pokémon that Great Balls just cannot manage. I tend to reserve the Ultra Balls for Pokémon I do not have in my Pokédex and want to catch them in as few a moves as possible to prevent them escaping.
I have not discovered a Master Ball yet but seeing as they have been present in previous incarnations of the Pokémon games they must exist right?