What are some of the accessories for these mics for.
elements
Omnidirectional - 360 degrees (good for small outdoor venues)
Cardioid - Looks like this
Sub Cardioid - What do these do?
Hyper Cardioid - for distance recordings??
Mini-Shotgun - What do these do?
For simplicity's sake, let's consider a diagram from zero to one. 'Zero' being fully closed(not really, but let's just say), and 'One' being fully open(or 360 degrees).
That various pickup patterns you mentioned provide pickup in various degrees and are affected, acoustically, in doing so.
Generally speaking, the pickup patterns go in this order from the smallest degree of pickup to the most(or 360 degrees)
0 ---------------------------------------------------------------- 1
Shotgun - Hypercardioid - Cardioid - SubCardioid - Omni
The closer you are to the sound source, the better it is to use a wider, more open pickup pattern. The farther you go (again, generally speaking), you'll want a pickup pattern that is more focused on a tighter angle (i.e. hypers, shotguns).
There's MUCH more to it than that, and each type of polar pattern has it's own properties. Many people like/dislike certain ones. The more degree of an angle you have to pickup noise (One), the more ambient sound will end up on your recording. With more direction, and a focused angle (Zero), you can position the microphone where and how you want it to pickup what best to your ears.
From there, adjust to taste...