How is social security taxed?

I am a few years away from retirement, but wondering -- when I go to the Social Security website, it says if I work until I am 67 yrs I will receive X amount and if I work until 70 yrs I will receive Y amount.  When I start collecting Social Security, will I receive the full X (or Y) amount, or when the check arrives will taxes have been taken out of it already? And at what percentage would I be taxed? Are state taxes taken out too? I am single in California.