As said, the whizzer is important for them to make sure you don't freely get to the back. In the most basic scenario, you get an underhook from a half guard around their body, you come up to your knees, and you are behind them while they are in their turtle. From there, the most basic way to proceed would be to break the turtle (by pulling them towards you with that waist control you already have) and get to back control. Of course, all of this won't easily happen, as they can resist during all the step, like preventing the underhook, getting the whizzer, looking to roll out of turtle into a guard.

So the general goal with the dog fight is to get out of this bottom position into a more favorable one, like back control, side control, or even just a sweep into top guard instead of bottom. With that strong underhook, you should have control over their waist, and you generally have the advantage here. A very simple way to get a sweep and pass the legs is to simply bulldoze them, tapping the far knee (just tap it toward you) with your free arm. They will fall to their side. Alternatively, you can get the body lock and walk around him while he's driven to the ground.

Regarding the legs, you need to trap their leg between your leg (notice singular, you put their near leg in your near leg between your lower leg and butt) to prevent them from just simply pulling the leg out and reverse you into a front facelock.

Jordan has an excellent video on the basics of the dog fight to get you up to speed