As with many things, there is more than one way to skin a cat. This particular skill can be learned in a sitting and we teach two methods at CFNFC.
Method 1: the emergency foot lock
Method 2: the fireman aka the stripper
The reason we teach these two methods is because they are the easiest to learn, the fastest to climb with and are the most secure without tearing your legs open. This method allows soldiers with packs to climb ropes, so getting yourself up the rope should be no sweat!
First, the lock offs:
The Emergency Foot Lock
To learn this method, you should start while seated on a 20 or 24" plyo box. Once you get the hang of it, you can stand on the box, make the foot lock then slightly swinging off.
While seated, cross your legs at the shins naturally and draw the rope in between your crossed legs. uncross your legs and keep your feet level and tight together. The bight created between your feet and the tension created is what locks you onto the rope. This is a method that can be used when you lose control of the rope high off the ground/floor to regain control on the rope quickly for a safe descent. This method is also used for an extremely fast ascent and descent. The lock is fairly superficial, which makes it somewhat unstable for long stagnant periods on the rope, but excellent when your grip is strong and speed is of the essence.
To learn this method, move back again the the seated position on the box. You want to drill picking up and releasing the foot lock repeatedly before attempting to climb. The only difference between this lock and the Emergency Lock is an out and around wrap of the rope, hence the name(s). You're going to pick up the running end of the rope with the top of your non-dominant(dumb) foot and swing your dominant (ball-kicking foot) around the rope and press the rope down next to your dumb foot while slightly raising your dumb foot. The key is keeping the feet level to maintain the bight.
Next, how to ascend:
Reach as high as you can on the rope (later, you can jump and grab the rope as high as possible). Lock your hands in and with the rope out front, swing your hips up like a knees to elbows, pull your legs all the way up to waist high and lock your feet in with either method 1 or 2. Once they're locked, stand vigorously on the foot lock to drive yourself up the rope. Your hands will end up approximately at your waist, then slide them up to max height, release the foot lock and repeat until to the top of the rope.
Next, how to descend:
The descent is dependent upon the type of foot lock. If you're using the speed/emergency lock, then all you have to do is slightly open your feet and the rope will start to slide between them. The faster you want to go down, the wider you spread them. Hand over hand is the preferred way down, but some folks slide (not recommended without gloves!). If you're using method 2, then it's a tiny bit more complex but gets much easier with practice. First, with your feet still locked in, you have to lower your upper body down enough to go into a squat. This takes the rope away from your legs. Then you open you feet and lower yourself rapidly hand over hand like with method 1.