What is the maximum amount of money that I can earn in a year in
California and do not have to pay any income tax for because it is
considered so little?

Considering if you are single, living in California, for tax year 2003:

Regarding your Federal Return:  if your Adjusted Gross Income (AGI) is
under $7,000, then you will pay federal income tax of $0 in 2004 for
tax year 2003.  The standard deduction for 2003 is $7,800 so you could
have up to $14,800 of EARNED INCOME and owe no federal income tax.

Regarding your California Return:
If your income is less than $10,220, not considering adjustments, you
are subject to no California income tax.

DO YOU HAVE TO FILE?
Call IRS Teletax Information at 800-829-4477, listen to topic 351 to
see if you have to file.  Generally, even if you are not required by
law to file, you have already been subject to income tax withholding
and a refund will be owed to you. (form i1040EZ, page 9)

If you have not filed for previous tax years and believe you are owed
a refund, you can still file for the previous 3 tax years.

Please remember that federal income tax is only a portion of the
deductions from your earned income, and other taxes and withholding,
such as state disability insurance, social security, and others, are
not refundable.

2003 1040EZ tax form
http://www.irs.gov/pub/irs-fill/f1040ez.pdf

Revised 2003 federal tax rate schedules
http://www.irs.gov/formspubs/article/0,,id=109877,00.html

2003 California 540EZ form
http://www.ftb.ca.gov/forms/03_forms/03_5402ez.pdf?46362

Revised 2003 California 2EZ tax rate schedules
http://www.ftb.ca.gov/forms/03_forms/03_5402ez_rate.pdf

Another detail just occurred to me.  If you are an individual who may
be claimed as a dependent on another person's return, then you will be
unable to claim the standard deduction on your own return, thus
increasing your taxable income by the standard deduction. So, the
revised figures for a dependent applies:

2003 income of $7,000 or less is subject to no federal income tax. 

2003 income of $7,150 or less is subject to no California income tax.

The IRS and the California Franchise Tax Board both offer telephone
filing, which makes filing easy and hassle free if you are eligible.

United States Internal Revenue Service
http://www.irs.gov/

California Franchise Tax Board
http://www.ftb.ca.gov/

Thank you!