The first Tuesday of every month is free, except July and August. Basic admission is as David Smith said. Basic admission does not include the butterfly pavilion or the traveling exhibit (currently that's the tattoo exhibit). There's also the California Science Center, which is in the same park as the Natural History Museum and is free except for the Space Shuttle exhibit and their traveling exhibit.
Right price is evasive...different sites give different rates
Directly from their website: Adult $15 Senior $12 Student $12 Child $7 These where rhe prices 2 weeks ago when i was there. There website also lists all of the special exhibit prices. Special edhibits are an additional charge.
Thanks! Your answer is awaiting moderation.