I was watching 101 Submissions the other night and I was amazed that none of the guys who got caught in triangles even <i>tried</i> the counter.
I've only been training since August, but this counter that our instructor taught us seems spot on to me.
The first thing to do is relieve the pressure of the choke. To do this, stand up with the leg that is on the <i>same side</i> as the trapped arm. Keep your other knee on the mat.
Everybody stands up with the opposite leg. This only makes the choke worse because by doing that you are driving your upper body (and head) deeper into your trapped arm.
There are a couple of "moving parts" that happen more or less at the same time. With the leg up, you want to turn and drive that knee down into the guy's chest. The leg that has the knee on the ground you want to go perpendicular to the guy's butt (sort of the way you do prop your leg under the guy's head in a tight S-mount).
Essentially you are turning into the choke, driving the knee that is on the same side as the trapped arm around his leg and into his abdomen.
Hand position: With the hand of the trapped arm, you want to grab the opposite collar (or trapezius, if you're fighting no gi) and bring your forearm across the throat (adjust depending on sparring partner versus tournament competition). Use that as leverage to bring your body closer and to work your way around his leg toward the trapped side.
You are essentially grinding and stacking. The important thing is to move your body in the direction of the trapped arm. Stack his body tightly so that he doesn't counter the counter by switching to an armbar and put him on his head as you work to "pass the triangle."
With your free hand you want to grab the pants or the hip to keep him from turning with you as you move around his leg in the direction of the trapped arm.
I don't know if I've described it well. I haven't seen this counter in any of the bjj books I own or online, but it's already done a lot for my triangle defense. Even if you don't get all of the parts right at first, it seems to have a lot of the right mechanics (i.e., stepping up on the trapped side, not the opposite site).
I'd be curious what some of you experienced jiu jitsu guys think of it. Of course the best triangle defense is to not get caught in one in the first place ...