My own approach is this: Huggies Overnights, Snug & Dry, and Pure & Natural diapers have seams down each side, between the wings and the leak guards. I start by tearing along those seams, going front to back (starting at the back is harder due to the elastic waistband). This removes the wings and the leg cuffs. With these gone, it's then easy to pull the elastic out of the rear waistband. Then, starting in the crotch on each side, I pull off the leak guards. This leaves you with just the diaper padding. Finally, I tear a slit down the middle of the backing. And then I place this in the middle of another diaper.
I'd add pics if I could. Maybe later. It sounds like a lot of work, but it goes very quickly once you've done it a few times.
Some people just poke holes in the back of the baby diaper and place it in another diaper. I find this very uncomfortable, as the baby diaper's elastic makes it bunch up. Further, with the leak guards left intact, excess wetness will be channeled to the front or back of the stuffer diaper, making less efficient use of the outer diaper's padding. If you don't want to tear the elastics out of your stuffer diaper, at least grab some scissors and snip them in 4-5 places on each side. That'll let the stuffer lie flat and will let excess wetness roll off quickly.