California has a non-partisan primary system. The top two candidates regardless of party advance to the general election. You can only get on the general election ballot by making the top two in the primary. No write-in votes in the general election for California governor.
According to Ballotpedia, the requirements for the primary are:
The number of signatures required for nomination papers are as follows:
- 65-100 for candidates seeking the office of United States Senator or a state executive office
The filing fee for a candidate seeking a seat in the United States Senate or a state executive office (e.g., governor or treasurer) is 2 percent of the first year's salary for that office. The filing fee for a candidate seeking the office of United States Representative, state senator, or state assembly member is 1 percent of the first year's salary for that office. The fee is paid to the California Secretary of State through the candidate's home county election office.
Or file a petition with
those seeking statewide office must file 7,000 signatures.
So if you do not want to get signatures, you can pay a filing fee of 2% of the governor's salary, which was $190,100 at the end of 2016. That would be $3802 if the salary stays the same.
For 2018, the period in which signatures can be submitted is between December 14th, 2017 to February 7th, 2018. It looks like the fee can be submitted until March 9th, 2018 or March 14th, 2018 if the incumbent does not run. It is possible to be a write-in candidate in the primary. The deadline looks to be May 22nd, 2018.
Any deadline may change for future elections. I would strongly suggest that you call the county election office and ask them about deadlines and requirements rather than relying on the posted deadlines. There may be additional requirements not listed.
Either way, signatures or fee, you would submit them to the chief election official in your local county government. You should be able to get more details from that person. Ballotpedia has a list that is too long to copy here.