After catching the first Pokémon you are left to catch Pokémon as you wish, with no further explanation on how best to catch these Pokémon.
After throwing around 10 balls and having them hit away/dodged and just rolling pathetically on the ground, I realised there must be a technique I missed.
How should you approach a wild Pokémon encounter so as to maximise catching probability?
You swipe the balls upwards to hit the Pokémon itself.
If you hold the pokeball you can see a green circle growing smaller, if you manage to land it inside the green circle you get bonus xp based on how small the circle is.
Also, according to some people you have a better catch chance if you catch the pokemon when the inner circle is smaller.
I hope this is clear, if it isn't just leave a comment and I'll try to explain better.
From the Pokecommunity guide (emphasis and hyperlink mine):
To throw the Poké Ball, tap and hold on the Ball. Circles will appear over the Pokémon, one which is coloured (said colour indicates how ‘catchable’ the Pokémon is; for instance, green = easy, and red = hard) and diminishes in size. You want to throw the Poké Ball when that target ring is as small as possible to increase your chance of catching the Pokémon.
To fling the Poké Ball, swipe upward directly at the Pokémon. You may need to use the full screen for your swipe, as otherwise the Poké Ball will fall short. Be sure not to throw it sideways! If you drag and spin the Poké Ball before you throw it, you can get a ‘curveball bonus’.
This is what I know so far: the difficulty is indicated by the color of the circle - from easiest to hardest: green, orange, red.
The catch rate also depend on how big the circle is and if you get it in the colored circle or not. If the colored circle is big and you get it in the colored circle then you get a "nice throw". If the colored circle is about half of the regular white circle then you get a "great throw" and if the circle is the smallest it can get and you get it right in the colored circle then you get a "excellent throw".
For a "nice throw" you get 10xp bonus, if it's a "great throw" you get a 50xp bonus, and if it's a "excellent throw" you get a 100xp bonus. I'm not 100% sure but I think if you get a curved ball catch then I think it also increases your chance of catching it, also you get a 10xp bonus for a curved ball catch.
