Carpooling is a great way to save transportation costs as well as enjoy some company on the way. It is also an alternative to public transportation for those who don't own cars, such as most students. Carpooling often implies shared commuting (a group of people making the same trip on a regular basis), while rideshare/rideboards are usually used for one-off trips.
The best way is to use the rideshare board on Craigslist, as many Davisites do. Other possibilities are PickupPal or CarPool World.
There is a ride board in the Memorial Union, just down the hall from the information desk -however hardly anybody sees it or uses it.
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The ASUCD Ride Board is gone now, correct? —BrentLaabs
Yet another possibility is ZimRide, as it interfaces with Facebook so you can both get a sense of the person you're ridesharing with, and have a way of broadcasting your ride (or ride request) via Facebook feeds. If you already have a facebook account, you can just use that to log in.
Now defunct, Davis Trans had a variety of transportation options, including both a ride board and information on public transportation.