A Student Pilot Certificate and a Medical Certificate (3rd class or higher) are required to solo an airplane. Applications for both are started online. The FAA websites have a lot of good information, however first-time users may find them a little tricky to navigate. Here are some links with helpful hints:
IACRA: The FAA's pilot certification application system (Integrated Airman Certification and Rating Application)
MedXPress: The FAA's medical certificate application system
PSI Services: The private company that administers FAA written exams
Step 1:
Register as an Applicant in IACRA
Remember your new Username and Password
Step 2:
Login to IACRA and apply for a Student Pilot Certificate
Remember your new FAA Tracking Number (FTN)
Step 3:
Meet with a CFI to complete application
Remember to bring your valid photo ID (Passport or Driver License)
How to get a medical certificate
Search for Aviation Medical Examiners
Search Tip:
Designee Types: AME
Search Criteria: Location Search
County: (Santa Clara / Alameda / San Mateo)
Unless you own an airplane, you'll need to rent from a flying club. Most flying clubs in the Bay Area require "renter's insurance" (aka, a non-owned aircraft damage liability policy) with a minimum of $20,000.
Typical renter policies have multiple coverage areas and require you to purchase injury/property damage coverage in order to get the club required aircraft damage coverage. The amount of injury/property damage coverage you get is a personal choice.
Two insurance companies that I've used previously for such policies are Avemco and AssuredPartners.
Airplane Flying Handbook (AFH)
Pilot's Handbook of Aeronautical Knowledge (PHAK)
Step 1: Create an account with PSI Services
You'll need your FAA Tracking Number
Step 2: Find a Test Center
Suggest Santa Clara, Union City, San Francisco or Walnut Creek
Step 3: Select the Private Pilot Airplane (PAR) exam and choose a date and time
You'll need an endorsement from a CFI to take the exam