Artemis BJJ (MYGYM Bristol), Can Sönmez, Bristol, UK - 15/06/2016
To secure the kimura from the bottom of half guard, start from a 'double paw' on the arm they're using to try and cross-face you. Slide one hand down to their wrist, the other wrapping around their elbow. Flare that elbow out while simultaneously pushing their wrist towards their leg. That should collapse the arm, enabling you to then reach over their arm with your elbow hand, gripping your other wrist to lock in the figure four. Alternatively, you can simply sit up and reach over to lock in the figure-four.
Either way, if they sit back and try to free their arm, you can move into a hip bump sweep, much like you would from closed guard. If not, curl your wrists in to prevent them straightening the arm. Clamp the elbow to your chest, then you can torque for the kimura as usual. If they hide their arm, you could initially try Xande's option from my favourite online instruction site, BJJ Library. Xande shows how even if they are hiding their arm, as long as you can get the grip, you can still harvest that limb. He does it by scooting his hips towards them.
Another excellent resource is Andrew 'Goatfury' Smith, well known for his expertise in the kimura, all to be found on his brilliant Hubpages sequence of tutorials. He suggests shrimping away to make space, then bringing your leg all the way past their head, until you can push off their hip (on the same side as their trapped arm). That should give you enough leverage to yank that free. He is also the source of that handy tip on collapsing the arm.
Teaching Notes: Lots to emphasise and change next time. The basic grip was causing some people trouble, so next time I might suggest grabbing the meat of the hand, to make sure people aren't compromising the integrity of their frames to secure the grip. Also, clamping elbow to chest needs emphasising too, people weren't doing that enough: I did say it, but I think I need to demonstrate it more clearly to highlight where your arms should be. Also, curling the wrists inwards, as well as gripping with the fingers and thumb over the top.
People were having real difficulty extracting their leg in order to bring it all the way over the top, so that needs more emphasising. That should be easy to solve though, as it is mainly a matter of shrimping out enough to create the space to get that leg over.