I would like to know the general process of admission to get into a UC. What do they look at? What do they need when applying? What factors do they take into account? (specifically for me: Does an upward trend in GPA from freshman year to junior year (2.6-4.2) serve as anything? Thank you.
http://admission.universityofcalifornia.edu/freshman/requirements/index.html
http://admission.universityofcalifornia.edu/freshman/how-applications-reviewed/index.html
http://academic-senate.berkeley.edu/sites/default/files/committees/aepe/hout_report_0.pdf
UCs use only 10th and 11th grade grades and give weight for up to 8 semesters of approved Honors or AP courses. GPA is the most important factor for UCs. The links above probably have more information.
Good advice here. Also, UCs now admit by major. Look up the data on admission by major for each campus on the UC website and choose wisely. If you are denied your primary and backup majors, you will likely be rejected from that campus even if your stats would qualify you overall. Some schools (e.g., UCSB College of Engineering) consider only the primary major. Getting admitted to UC as Undeclared used to be a good way to go. Now the departments have blocked most changes of major into “impacted” or oversubscribed majors.
Ninth grade is not counted in the UC GPA. However, when you apply you will need to list classes such as Algebra 1 or Geometry, English, US Government, foreign language, etc. that will satisfy UC “A through G” admission requirements. Getting a D in a required class may disqualify you unless you retake it in summer school. Plan to get an A.
Study well for the SAT and ACT. Take both. Some students do better on one or the other; UC will use the most favorable single sitting.
Strongly consider your local community college honors program. You can start college in small classes for very little cost. If you do well, you can arrange guaranteed transfer (TAG) to a UC campus as a junior. Your diploma will say “University of California.” This pathway bypasses all of the admissions craziness, or rather, defers it for two years! 
Best of luck.
UCLA/UCB also use fully weighted UC GPA along with capped weighted UC GPA.
https://rogerhub.com/gpa-calculator-uc/
Upward grades trends will be noted so explaining your low grades in your personal insight essay can help.