Cardioid - Picks up mostly what is in front of it, but more of the sides than most of us want to think about. If you're doing live sound, most mics will be cardioid like the trusty SM58 shown.

Supercardioid - Tighter in front, but don't forget that nasty lobe in the back! Especially for placement near a wedge monitor, be sure to face the wedge slightly off to the side, not directly in back of the mic. Hypercardioid is similar to supercardioid, but the lobes are slightly different. The mighty Beta 87 is a supercardioid.

Omni - Should pick up uniformly all around. Pray you never run into them in live sound work. I've worked for video guys who have no idea about audio/mics/polar patterns and order omni lav mics. Trying to explain to them why you can't get enough gain before feedback results in "deer in the headlights" looks.

How to tell? Super/regular cardiods always have vents in the back to create their patterns, an omni has no vents.

The young lady on the left is covering the vents on her mic with her hand, effectively turning her directional mic into an omni, and making life difficult for the person doing foh.

The other 2 two are making it much worse!