The Underhook
Probably the most common way to control your opponent. If you ever wonder where you're arm should be then the underhook is a good guess. Basically an underhook means that I place my hand under my opponent's armpit. In the left picture the handsome guy in the black and red shirt is utilizing the underhook from half guard and butterfly guard.
The Whizzer
To counter the underhook I hook with my hand around my opponent's under hook.
In the pictures you can see how to use the Whizzer from butterfly and how your oppenent can use it, to counter your half guard game from the top.
The Gable grip
Holding your hands palm to palm without the use of your thumbs. a very storng and highly used hold.
In the left picture you can see it used in an head and arm control from the side
The G-grip (also know as Guillotine-grip)
Holding both palms faching your body, the upper hand is closed around "the fat of the hand"( the area between the little finger and the palm).
This grip is usually used for Guillotins and for back control (see the Seatbelt). In the right picture you can see this beeing used in a standing Guillotine
The S-grip
I grip my hands together closed in a fist, with the fingers of one hand inside the fingers of the other one.
In the right picture you can see me using it as a step to secure an arm triangle
The Seatbelt
This is a position in which the both hands are around the neck and chest of my opponent (same as a car seatbelt). One hand should go over the shoulder and the other hand as an under hook. The hands are closed in a G-grip. The upper hand in the grip is always the under hook, this way the choking hand is near the throat and is more protected. Notice that the chest must be tight to the back of my opponent
In the right picture you can see me use the seatbelt to control the back. In the left picture it's used to secure a back position from the sprawl, (Notice that the hands should be in the middle of my opponent's body, but were moved to the side in order to show the grip).