First takedown:
1. you have your a firm grip of your opponents gi at the elbows with both hands
2. with your right hand pull her left arm toward you and up so it clears your left shoulder
3. turn your back into your opponent while lowering your center of gravity (squatting slightly in setup for the throw); pull her right arm down and across your body; pull her left arm up and over your back
4. uncoil the spring (straighten your legs from the semi-squat position) and pull your opponent forward to throw them over your back
Second takedown:
1. you have your opponents right lapel in your left hand and their left sleeve at the cuff in your right hand (grip with a fist - not with your fingers curved around the edge of the cuff).
2. while pulling her left arm forward; pull your own right hand in, bending at the elbow, toward your own right shoulder then circle your entire arm around her arm finishing the movement by lowering your center of gravity and ducking elbow first and then head under her left arm
3. you should end the above movement with your left knee on the floor between her feet; your right leg extended fully and based out to your right; the left side of your head firmly against her left latissimus dorsi and MOST IMPORTANTLY - her left arm securely locked between your fully bent right arm and your torso.
4. fold your left leg underneath your body and sit back forcing your opponent to summersault over you and onto her back in front of you - then quickly get side control
Escape from half guard:
1. your opponent has you in half guard; they also have underhooked your left arm and have curled tightly underneath you with their neck protected and their head against your left knee
2. circle your right arm around their left arm from the outside and secure it tightly against your body - grab their left lapel if it helps you keep the arm locked tightly in this position
3. as if you were to connect the inside of your elbow to their adam's apple - hook his head and then walk your fingers out effectively uncurling his head and body so he is stretched before you instead of under you as he was
4. pull your leg partially out from the half guard resting your right knee now on his thigh - put the majority of your weight on this knee - your other point of contact is your right shoulder and chest pinning his left shoulder and chest to the floor
5. let go of the left lapel and base your right hand on the floor in front of his right thigh - push your hips forward, pull your right leg free from the half guard and swim your right hand under his right thigh - basing it on the floor; switch your hips and finish in a sprawled side control position
If you've gotten free of the half guard but are prevented from passing to side control because your opponent has braced his bent leg between his body and yours:
1. get a good base and sit back a bit on your heels
2. grab his gi trousers at the knee firmly with both hands and push his bent leg to the floor and pin it there
3. get to your feet but stay low using your body weight (contact points being both your hands on his gi trousers at the knee and your shoulder/upper arm and body on his upper thigh) to keep him pinned on his side
4. bring your knees/base back in tight against your opponent in standard side control with one arm securing against his leg to prevent him from getting you back into guard or half guard and the other arm securing his upper body/neck/shoulders
5. if your opponent rolls to the side in an attempt to get to his knees you can easily just keep control of his legs with your grip on his gi trousers and then, using your body weight to pin him (your point of contact being your shoulder on his upper thighs or bum) down and take his back.
Any clarification or correction of these techniques is most welcome - it's a lot to try and remember.