There are specific yeast strains that for that style. You could use any lager yeast at ale temps, but I think you would get too many esters and off flavors. Try White Labs WLP810 or Wyeast 2112. I've used WLP810 in a CC and liked the results. Try to stay in the cooler end of the yeast's range for less off flavors. A swamp cooler works fine, as you usually don't need much of a temperature drop from room temp. Around 60-degrees or so should be good.
Pretty easy to make and very forgiving with the fermentation temperature. As mentioned, there is a specific yeast for California Common beers. Use that yeast and you are good to go. I would not let the fermentation get to 70˚F or higher.
Imperial Vanilla Stout
Triple B Barley Wine
Arrogant Bastard Clone
Imperial Red Ale
Try Anchor Steam for a commercial example. Use Wyeast California Lager, or White Labs San Francisco Lager. AS uses Northern Brewer hops, and, yes, it's good and worth brewing. If possible, keep ferm. temps in the lower 60s F.
Thanks for the help! I am definitely going to try one of these out for my next brew. The lady friend is a huge fan of some of the more bitter lagers, so I think I'll try to show her a different take on them with this style using plenty of hops.
My experience has shown me that the Cal Common style (a la Anchor Steam) is more a product of the Northern Brewer hops they use and not the yeast or temp. I make an Anchor clone using all US Northern Brewer hops fermented with US05 @ 65-69 that tastes very close to Anchor Steam and is quite a departure from other West Coast pales and IPAs that use the citrusy hops.