You will need to take and pass a hunter safety class (schedule at DFG's website--see link below )and then buy a hunting license. If you browse through DFG's website, you'll find a lot of useful information.
https://www.dfg.ca.gov/huntered/
Here's a link with dove and other season dates for other upland and big game in CA. You can find the same information on DFG's website but this has it all on one webpage.
https://www.wonews.com/t-Hunting_Calendar_022213.aspx