Gracie Barra Bristol, (BJJ), Can Sönmez, Bristol, UK - 31/05/2012
There are three main approaches to pass the closed guard (I should note, I'm still pretty crap at all three, even after six years ;D). The first option, and probably the hardest, is to go from the knees. This has the advantage that you are less likely to be swept, but you're in much more danger of being submitted. As is so often the case in jiu jitsu, posture is very important: if you reverse engineer the lesson on maintaining closed guard, that means you don't want them to grip your collar or get a hold of your head.
Stay upright, back straight, head up. Also don't let them bend your arms: keep at least one of them stiff into their hip. It is very important to control their hips, as they need to angle off to attack effectively. Your other hand is ready to push them down if they attempt to raise their torso towards you, or more typically, gripping both collars and keeping their back on the mat.
For a strong base, widen your knees, sitting on your feet. Alternatively, you could try squeezing your knees to their hips to stop them moving, but that will result in a less sturdy base. Make sure you do not put your elbows on the outside of their legs: keep them inside, or they can start kicking up into your armpit for triangles, armbars, flower sweeps etc.
Another way they'll be looking to disrupt your base is to angle their hips away. To prevent that, you can simply follow them, making sure you keep squaring back up so they don't have that attacking angle anymore. You could also try caging their hips by squeezing your knees together, but that can result in a less stable base.
You can pass the guard from the knees, but personally, I've always found that incredibly hard. Most of the time, to have any chance of passing you'll need to stand, bringing gravity into the equation. This is therefore the second approach for passing the guard. Ideally before you stand, it's useful to grab one of their sleeves: I'd suggest grabbing their sleeve with the hand you want to press into their hip, as then you can accomplish two goals at the same time. It also very helpfully means you'll be able to step your foot up on that side with impunity, as they can't use their arm to attack it.
There are a few different ways to stand up. First, you can simply post your hands on their torso and jump up. That's fast, but it leaves you open for attack if you aren't able to swiftly get your posture once you've stood up. A second, more gradual option is to swing your head towards your collar gripping side, then step up your foot on the hip pressing side. You can then twist your other foot to help you stand up, or just get to your feet: it depends on if you need that intermediary step.
Once you've stood up, thrust your hips forward, head up and back straight. You don't want to be bent forwards, or they can break your posture down. Also try to maintain a hold ideally on their sleeve, or failing that, their gi or belt. Your goal is to have them squashed on the floor, unable to easily move their hip. The best situation would be that they're 'stacked', which means they're squished up onto their neck. Obviously be careful if your partner is smaller than you and in that position, as you never want to put a lot of stress on a training partner's neck.
Naturally it isn't going to be that easy to either open the guard or even stand up. In order to attack, they are going to want to disrupt your base and break your posture down. The first way they'll probably do that is to establish a strong grip, on your sleeve and collar. You don't want that, so try to strip any grips before beginning your pass. Not to say that it's impossible to pass if they've got grips, but you'll find it easier if they don't.
If they grab your collar, use both of your hands to grab either side of that sleeve or wrist. Push it forcefully away from you, while simultaneously leaning back slightly. If you remember the grip break from the maintaining closed guard lesson I taught a while back, this is a similar principle, but from the opposite position. Another option is to put both your hands on their gripping arm, trapping it to their torso. Posture up forcefully to break the grip.
If they get a grip on your sleeve, then grab their sleeve with your free hand. To break the grip, yank your trapped hand back as your gripping hand drives forward. TrumpetDan has a good video on this, here. I don't generally recommend YouTube, but he is one of the better teachers on there. A simpler option is to circle your hand either inside or outside of their arm, then chop downwards to break the grip: there is a good explanation of that in Beneville's excellent Passing the Guard.
Should they get a hold of the material by your knee, you can use a similar grip break. Grab their gripping wrist with your same side arm and press it to the mat, then kick your trapped leg back. Ideally, as with the previous grip break, this will now give you control of their arm, which you can immediately use to initiate your pass.
When standing, there is another basic option you can try if they attempt to hook your foot. Kick your foot forward and out to break their grip, then put it back down out of their reach. This is particularly effective if they are only grabbing behind your heel, slightly less so if they have a firm grip of the gi material. It is also advisable to step a leg back to prevent them from having the grip available. Another possibility, which TrumpetDan suggests, is to simply turn your foot inwards, to prevent the handstand sweep.
The third option for opening the closed guard is perhaps the simplest, but also the most risky: bait a submission opportunity. The idea is that you make them think they can get a submission where they have to open the legs (e.g., triangle), but carefully prepare your frames. That way, as soon as they open their legs for the attack, you can capitalise and begin your pass. This means you don't have to work to get their legs open, but it puts you in a lot of danger if you aren't good at escaping submissions. So, I wouldn't recommend you try this until you're very confident in your defence.