Artemis BJJ (MYGYM Bristol), Can Sönmez, Bristol, UK - 05/12/2016
In half guard, your first concern is to stop them flattening you out and starting their pass. They are generally going to want to establish an underhook on their trapped leg side, using the other arm to control under your head. In many ways, it is a similar position to standard side control. That will enable them to crush you to the mat, then exert lots of shoulder pressure to kill your mobility. Many of the same attacks from side control can also be viable from here, like an americana.
Naturally, you don't want them to reach that dominant position. Your goal is to get up on your side, with your own underhook around their back, on your trapped leg side. That is one of the main fights you'll have in half guard, so it is essential that you get used to working for that underhook.
If you can get the underhook, that accomplishes two things. First, it prevents them crushing their chest into yours, which would help them flatten you out. Second, it means you can press into their armpit to help disrupt their base, as well as help you get up onto your side. You can use your knee knocking into their bum at the same time to help with this too, as that should bump them forward.
For your leg positioning, the standard half guard is to have the inside leg wrapped around with your foot on the outside. Your other leg triangles over your ankle. This provides you with what SBG refer to as a 'kickstand': that outside leg is useful for bridging and general leverage. It's harder for them to flatten you out if you can resist with that kickstand structure.
After you've controlled a leg, got the underhook and onto your side, you want to block their arms. Almost a decade ago, Indrek Reiland put together an awesome video (made even more awesome by being free) about the fundamentals of half guard. The main principle I use from Reiland is what he calls the 'paw'.
By that, he means hooking your hand around their bicep, just above the elbow. You aren't gripping with your thumb: this is just a block, to prevent them getting a cross-face. Reiland emphasises that preventing that cross-face is the main principle. Therefore, if you can feel they are about to remove your paw by swimming their arm around, bring your underhooking hand through to replace your first paw with a second: this is what Reiland calls the 'double-paw' (as he says in the video, it's an approach he learned from SBG black belt John Frankl).
Similarly, if they manage to underhook your underhook, bring that arm over for a double-paw (this is also applicable from the start, if you're framing against their neck), then work to recover your underhook. Keep in mind with the double-paw that you need to make sure you don't leave space under your elbow. Otherwise, as Reiland demonstrates, they can they go for a brabo choke. Get the elbow of your top double-pawing arm to their nearest armpit, as that makes it easier to circle your arm around to their back.
If you've been flattened out, then I find it is easiest to try and recover closed guard. It's generally more efficient to shift your leg positioning for this, bringing your outside leg over and hooking their leg, inserting your instep underneath their shin too. That leaves your other leg free to be pulled out. Curl your body towards your non-trapped slide, aiming to get an elbow inside their knee. Pry that open, while simultaneously attempting to wriggle your leg out. Once you get your knee/shin onto their thigh, you can square your body back up, using that knee/shin for leverage.
From there, it's the same technique as recovering closed guard from side control or mount. Hook your arm just above their elbow and grab your opposite collar/shoulder, to stop them pushing your knee down. Get control of their head with your other arm. From here, keep shrimping until you can bring your legs around their back for closed guard: how much you need to shrimp will depend on your flexibility. Going to open guard is fine too: butterfly can feel natural from here, but only do that if you feel comfortable with butterfly guard, of course.
Particularly for guard recovery, Braulio's alternative to the paw is a good option. Instead of hooking around their arm, he just 'facepalms' by putting his hand on his forehead. It's surprisingly effective at blocking their crossface, because they have to somehow get past your arm first. With that facepalm defence, you can dig underneath and get closer to their leg, ready to pry their knee away to recover full guard.
Teaching Notes: Another simple class, I can't think of anything to add (especially as I'm writing this up two weeks later). I'll take extra attention next time to see if there are any tweaks I could make.