This is a look at the basic Cross Collar submission from guard. This is one of the first lessons taught during out Closed Guard block. You can see that I focus on breaking the posture using the core muscles instead of pulling with your arms. This will save your grip strength for when you're actually choking your opponent.
In addition to breaking posture this video really emphasises the importance of good hip movement. There are tons of legimiate setups for the Cross Collar Choke and there are tons of acceptable hand grips, there are different choking concepts and most of them are great. What I wanted to do with this particular technique (and lesson) is focus on lateral hip movement. You may feel that there is a lot of extra hip movement, and in a sense you are correct. I exaggerate the hip movement, as well as the grip entries, to help the student build fundamental basics that can apply everywhere.
Keep in mind that the pocket for your hand to enter into the choke will appear and disappear based on your hip movement. Try to avoid pushing up on your opponent to make that space and instead move your body. You will notice that the first time I do this on the video I enter with my fingers pointed towards his face. I did this for ease of talking to the camera but keep in mind it will be much easier to enter at the back of the head. I'm not saying you cant enter at the face, just that it will be easier in the back.
Take note of how I talk about the strong grip and holding the back of the collar. If you open your hand and your fingers can touch under the collar then chances are you are going to choke your opponent. The more space between the fingers the more space he/she has to defend.