Breaking out of the clinch
Perhaps the most overlooked aspect of MMA-style training. Most of us are taught that once you clinch you stay there or work to the ground. you may be better at striking and he better at wrestling, in which case it would suit you best to be able to break out of the clinch so you can strike. If you are a grappler, breaking out of the clinch may give you a better opportunity to set up a better takedown option.
Breaking out of double overhooks
His head is to the R of yours. Your R hand circles down and between your body and his arms and body, coming around to the right side of his neck. Form the wedge by hooking your R hand onto the R side of his neck. Your elbow should be forward of your hand; if it is behind your hand, he may be able to pass your elbow and get your back. Use the wedge to push him away, creating space and extracting your L arm. Put your L arm on his shoulder and push him away with the L hand and the R wedge.
Breaking out of double underhooks
His head is to the R of your head. If there is space, put your L hand in and cup his R ear with your palm (the "ear muff"). If there is no space bring the thumb side of your hand up next to your R temple, quickly move your head to your L and slip your L hand between your heads, once again cupping his R ear with the palm. Use your L hand to push his head away, creating space to put the wedge in with your R hand as above. Use both hands to push him away.
Breaking out of One over, one under
Free the overhooked arm as for double overhooks and get the wedge. You should now be in a good position to push him away.
Breaking out of Thai clinch
Your first line of defense is to pull your shoulders up and turtle your neck. He cannot get a decent Thai clinch if you do that. Make sure you keep your hips close to a Thai fighter to avoid getting kneed.
If his Thai clinch is not good, you may be able to pummel through, one arm at a time, and get your own Thai clinch.
If he gets a proper grip, pulls your head down to his chest and it "goes dark", reach over and around his head with your R hand to grab near his R ear. Grab under his R elbow with your L hand, Circle step back with your L foot, and "turn the steering wheel", pulling down with your R hand, pushing up with your L, Hopefully this will create enough room for you to pummel for your own Thai clinch, or to push him away.
Shoulder pressure - Two in one, wizzer
Two on One
The important grip is the one nearest his shoulder/armpit.
Practice against him grabbing your head in a single neck tie with his R hand. Grab the crook of his elbow from above with your R hand, pulling it down. Step back with your R leg and turn, drive your R shoulder over and on top of his shoulder to pop his hand off and get Two on One. Experiment with the position and controlling and moving him with shoulder pressure.
Break away from Thai clinch to Two on One
He gets the clinch. His R foot is forward. Grab the R side of his head with your R hand, step and turn the corner with your L foot behind his R, pulling down on his head with your R and driving your L shoulder over and down onto his R upper arm. breaking his grip. You are now in a good position to grab a two on one on his R arm, push him away, knee him, kick, etc. etc.
Two on one to high single leg
Hopefully reasonably easy to understand. Do it properly your head is on the inside and the arm that was caught in the two on one is trapped between you while you get the single leg.
Lots of other options from 2 on 1.
He gets an underhook on your R with his L. You nullify an attempt to go to your back by clamping down with you R overhook. Circle step back with your R as you apply pressure on his L shoulder with your R.
If you get the underhook, slide the hand a little out along the upper arm past the deltoid, do the circle step and shoulder pressure similar to the overhook wizzer. Moving the hand out along his arm gives you greater leverage on his shoulder.
Revisiting breaking out of the clinch, incorporating shoulder pressure
With any of the break out options above, except the Thai clinch, where you get the 2 on 1, you will end up with the wedge, and either the over or underhook. From here, you can circle step back and apply wizzer pressure with either the over or underhook to move him around and disrupt his balance.
With shoulder pressure, say with your L arm hooking his R, it is a short logical step to push his shoulder down, spin him, and then secure his head with a guillotine or front headlock with your R arm around his neck.
if you wish to avoid grappling, just sprawl or semisprawl on top of him pushing his head down with your chest until your hands touch the ground. John calls this the Touchdown. Once you get the touchdown you can disengage if you wish by putting your R hand on the back of his neck, the L hand on his R elbow, doing a push up and breaking away, with a good shot at the head if both his hands are still on the ground.
Other grappling options from the Touchdown are to armdrag his R arm with yours and go to side back control on his R side with a seatbelt/harness grip (L arm over his L shoulder, R arm under his R armpit), rolling half nelson lapel choke, gator rolls, etc.
Linking Roundhouse Kicks and Takedowns
Getting away from the "three-coach model" where you train standup, clinch, and BJJ on different days with different coaches.
The setup stance needs to allow you to move in a straight line to secure the takedown. Having to go in an arc or turn a corner to get your penetration step will not work as well.
Setting up a Double leg with an outside thigh kick
You both have your L foot forward. Line your L foot up between his feet. Kick his outside L thigh with your R shin; bring your R foot back, put it down just behind your L foot so you have the range to shoot. Change level, shoot, penetration step with your L foot, grabbing behind his knees for a double leg.
Setting up a High Single leg with an outside thigh kick
You both have your L foot forward. This time,line your L foot up with his L foot. throw the R kick to his L leg, change level, step in on the kicking R leg, follow with the L, bumping him, head on the inside and picking up his L leg trapping it between both of yours. Proceed with the takedown.
Setting up a Double leg with an inside round kick
You both have your L foot forward. Line up your L foot between his feet. Generate tension in your legs by isometrically pulling your L foot back and pushing R foot forward (without actually moving the foot). Suddenly release the tension and fire your L kick at his inside leg (for practice, the kickee can turn his L foot out, offering the calf as a target and this avoiding shin on shin). Change level, step straight in between his feet with the L kicking foot, grab his knees and execute your double leg.
Setting up a high single leg with an inside round kick
You both have L foot forward. This time line your L foot up with his L foot. Fire the kick as above. This time, bring the L foot back just behind the R foot, change level and shoot with the R leg, bumping him and grabbing his R leg, trapping it between yours. Finish the high single from here.