Miura-ori Fold
Start here! This fold is the easiest and learning it will equip you with the skills to fold the other, more complex patterns. Better video coming soon!
Modified Waterbomb
This fold uses the same techniques as the Miura-ori but mixes up the directions of the zig-zags a little bit.
Sequent System
This is basically a thin Miura-ori (like a bellows) combined with a column of squares.
Square Twist
This one is difficult and completely different than the others. Invented by Ron Resch. Play with a digital simulation here to better understand it.