The knee sweep is used when a guy tries to stand up against your butterfly or sitting guard. You are in butterfly or sitting guard with your back on the mat (a no-no, but it happens). The guy is on both knees looking to stand up and pass.There's also an entry to the cross guard, or X-guard as Marcelo Garcia calls it, off the Fugitive here. Scroll down toward the bottom of the post to the paragraph beginning "The cross guard sweep goes like this."
You are trying to control the wrists (remember Marcelo’s point “they try to pass with their hands”). When the knee goes up, grab the ankle with the hand on that side, and flare your leg on that side with your shin in the crook of the guy’s knee. Your other hand should be attacking or controlling the opposite wrist.
Pull on the ankle and push out with the knee. One detail that Rodrigo pointed out was tha the knee should be pointing out at 45 degrees, not straight up.
You can also push with the outside hand on the guy’s wrist. It is a sort of pull-push when it works well. Scissor your legs in the sitting-guard-to-standing style ...
Guys have been standing up out of my closed guard lately, which gives me a great opportunity to attack early with The Fugitive or late with the transition to cross guard and the cross guard sweep. I've been a little too dependent on the Superfreak and Omoplata sweeps of late--though I like the fact that I've put a priority on "Scissors" and "Crimson" (of Scissorhands and King Crimson, respectively).