Sarah:
There are three major things that can contribute to Corning Ware staining, and two of the three are related by a common factor: surface erosion.
Some chemicals, like over-use of bleach and acidic substances, can etch the surface. Once it's etched, it can hold stains pretty readily. There is not a whole lot to be done here; etching on Corning Ware is pretty much permanent.
There is also mechanical abrasion; this usually comes from cleaning with things like scratchy cleansers or cleaning pads. Cleanser isn't nearly the problem it used to be; most have been reformulated in recent years to be much gentler than before. Today's bad boy is the green Scotchbrite pad, which is evidently intended to remove barnacles from ships' hulls, it's so scratchy. Use the scratch-free BLUE Scotchbrite if you want some scrubbing power on Corning Ware. However, like etching, abrasion on Corning Ware is not removable once it occurs.
The other situation that can lead to stains is mineral buildup. The buildup itself can appear to be a stain, or its slight roughness can give other stains something to "grab" onto. Mineral buildup is addressable; you can use Lime-Away or CLR on the piece to get it shiny again. After the mineral buildup is gone, washing and drying the piece by hand can help to prevent recurrences if you're in a hard-water area like I am.
Hope something in here helps.