There are many private universities available in California.
Visit http://aiccu.edu for The Association of Independent California Colleges and Universities.
For out-of-state universities, you will want to visit the specific school's website for entrance requirements, campus information and how to apply. Most will have their applications on-line. You can also use Naviance to view college and major information.
Many private universities require a counselor and/or teacher letter of recommendation. Make sure to give your counselor/teachers at least 2 weeks notice when asking for a letter of recommendation. Be sure to give them a resume or the Counselor Letter of Recommendation request form so they have the most complete information about you. This form is available from your counselor.
The Common Application
More than 400 colleges/universities use the Common App. The website is http://commonapp.org