I applied to 7 colleges when I was in high school. Most of the time, for private schools/out of state schools, you can send in the same application through the Common App. In the Common App, you basically just fill out your extra-curricular activities, volunteer experience, and an essay about yourself. Certain schools may ask you to answer additional supplemental questions with the Common App. I remember one supplemental question for Stanford was: Write a letter to your future roommate to introduce yourself. So once you fill out the main portion of the Common App, the supplemental questions for each school will take you a little longer depending on how many schools you apply to.
The University of California (UC) system has their own application system but it is very similar to the Common App. I found out that I could reuse my essay from the Common App and apply it to my UC apps. After completing the UC app, you simply just check which UC schools you want it sent to (UC Berkeley, UCLA, UC San Diego etc). So you just need to fill out 1 app for any of the UC schools. Keep in mind, there is a fee for every application you send out which could range from $70-100 each.
I think 6-8 colleges is a good number to apply to and seemed to be about the average for my classmates. I suggest taking college visits/tours of colleges that interest you. See which schools fit you in terms of the school culture and academics. Don't be afraid to take chances and apply to colleges that might seem to be a reach for you. I personally never expected to get into Stanford but thankfully my dad convinced me to apply. The whole application process took me a few months to complete, which included writing my essays and getting people to proofread it so give yourself enough time so you don't feel rushed.
Hope this helps!