If you had sufficient income to meet each state's filing threshold, you will need to file tax returns with both states.
You will want to file an Idaho part-year resident return. You should be able to obtain a tax credit on the portion of your California income earned while an Idaho resident, to offset the burden of double taxation.
Your tax situation in California is actually a bit more complicated, and may require the filing of two returns, as your were a non-resident for the beginning of the year, and a part-year resident once you assumed California residency. You may wish to consult the California Franchise Tax Board to determine the best way to file. http://www.taxes.ca.gov/Income_Tax/index.shtml
