(Sometimes they are thrown back in disgust, but too often they are kept by people who have to keep everything, whether or not they eat the fish.  They give the fish to a neighbor who promptly sticks it in the back of his freezer, only to toss it out months later while defrosting.  This happens all the time from San Pablo Bay through the Carquinez Strait, all the way to where Suisun Bay receives the Sacramento River.  Small wonder they are rarely caught in good sizes any more.)

But you can indeed fish for them "on purpose" if you know where to find them and what they eat.

Flounders are dependent on the estuarine environment within the bay system.  As soon as the cold temperatures arrive they migrate from relatively deep water in the ocean to the shallow sandy or muddy bottoms of the wetlands.  Authorities differ on the exact range of the spawning season, but it is safe to say that prime fishing time is from December through March.  Flounders have a remarkably high tolerance for fresh water and can be found in Montezuma Slough and as far upriver as Rio Vista.  Generally speaking, however they are located during the spawning season in waters like sloughs, lagoons, bays and river mouths at depths of twenty feet or less.   Find a place where fresh water empties into a bay and you may be in business.   Some good shoreline fishing can be accomplished in Martinez,  Benicia, Rodeo, Vallejo, Point Pinole, Butler's Beach, and the Berkeley Flats.  When the spawn is over the adults move back to the sea.  Fishing is less productive but still possible if you can find a sandy bottom with a depth of 50 feet or more.  Adults can go down to 900 feet in the summer months.  The young remain in the estuary system.

Young flounders eat worms and small crabs or shrimp.  Older flounders will go after bigger crabs and fish like perch.  So your bait offerings should be similar.  I've found the best baits in the Bay to be blood worms, pile worms, grass shrimp, and cut anchovies, in about that order. 

By far the best rig for flounder is the sliding sinker rig:
This is one time you should pony up for some first rate  sharp hooks like Gamakatsu or Owners.  Sizes range from #6-2.  Go with what makes you feel comfortable and keep in mind that bigger hooks mean less chance of getting swallowed. The flounder's bite is a finicky tap-tap, almost like a staghorn sculpin's, very light yet persistent.  Sometimes you will get a straight tug and side charge when the fish is hooked but more often than not you need to be ready to set the hook yourself.  Let the fish nibble, even play out some line if you like, and then give it a firm yank.  As always, keep the line taut, not an easy task for a fish that runs helter skelter from side to side.