Can i claim my trailer that i own and the rent i pay every month to sit it on the lot in a mobile home park, i also pay taxes on the trailer. what can i claim

If the trailer has a kitchen, toilet and sleeping quarters it is considered a second home.  You can deduct mortgage payments and any property or personal taxes if you itemize. If your state has a rental credit you can claim your space rent. 

I live in San Diego California. How much credit can I receive from claiming my manufactured home lot rental on my state income taxes?

California rental credit is $60 if filing single and $120 if filing married jointly. See details here:

https://www.ftb.ca.gov/file/personal/credits/nonrefundable-renters-credit.html