Four Basic Ways to Pass the Guard
Left, Right, Over, Under
Passing the guard can be quite a challenging task (some would argue that it's the toughest action in all of jiu jitsu, and I would be hard pressed to disagree). The guard game keeps developing and evolving, and to say that it can be tough to keep up is a huge understatement. However, there are a few different ways to simplify things, starting with four "directions" in which you can pass: you can pass to the right, or to the left; or you can go over the legs or under the legs to pass. That's really it, unless there's something about the laws of physics we're missing (there usually is).
Starting in your partner's open guard, dive both arms under your partner's legs at the same time (one at a time often leads to a triangle). Next, clasp your hands together at your partner's waist, pulling them onto your lap. This will take away their most basic guard maintenance actions. Reach across to your partner's far collar with one hand while controlling the pants with the other hand, with the general idea of putting your partner's knee into their nose. Turn their hips away while doing this, and finish by settling into 100 kilos side control.
Start by opening your partner's guard, or just begin in combat base, with your left knee up. As your partner's hips begin to turn in toward you, use the fact that their left thigh will be lower than your knee to cut your knee across their thigh, pinning their left leg to the mat. As you slide your knee to the ground, turning your hips to your right, attain the underhook with your left arm. Next, take either sleeve or head control with your right arm, ultimately pinning your parnter's shoulders to the mat. Free your leg last. For more details on the knee cut pass, check out this tutorial.
Once again beginning in combat base, leading with your left leg, as your partner's hips again turn to face you, their right knee drops this time. Use this opportunity to "staple" their leg in place with your shin, driving forward and across their leg, keeping your foot on the inside for now (mirroring the knee cut pass, but to the other side). As you slide your left knee forward, lift your right foot up to avoid any scissor shenanigans. Next, look to attain head control, helping to gently encourage your partner to look away from where you want to finish the guard pass. For more details on the leg staple pass, check out this tutorial.
Finally, you can pass your partner's guard by going over both of their legs. Start standing, and take pants grips on the inside of your partner's knees. Pressure their knees in toward their chest, making sure to really put your weight in, prohibiting any sort of fundamental guard maintenance or entries into spider guard. While keeping constant pressure with your hands, you can either drop your shoulder down to your partner's solar plexis area to keep controlling them while you pass to the side, or you can pass directly to knee on stomach. For further information on the development of this guard pass, check out this tutorial.
Which direction is your favorite?
That's All, Folks
Brazilian Jiu Jitsu is an incredible mish-mash of information, and looking for help can often be like drinking from a fire hose: you often get more info than you want, and it can be really confusing. Methods like this (left, right, over, under) can be extremely useful in categorizing and simplifying your understanding of jiu jitsu, and you can often use this type of study aid to help you figure out your own (often unexpected) solutions! As always, please let me know how these techniques are working for you. It is always gratifying and incredible to me to hear that one of these tutorials has helped you from across the Internet!