You file a non-resident Colorado return. You only list income that was earned or paid to you while living or working in the state of Colorado. For example, if you worked in Colorado for one week for training, you would list 1/52th of your income as Colorado income (even if you were only staying in a hotel and California is your real permanent address). You have to tell Turbotax how to allocate your income, the program can't do it by itself. You will get credit for your taxes withheld in Colorado which should result in a large refund.
Then you file a California resident return, which reports and pays tax on all your world-wide income. If you did have some Colorado income and pay some Colorado tax, California will give you a partial credit for those taxes. For example, suppose you make $2000 per week and worked one week in Colorado. Colorado's income tax rate is 4.4% so you would pay $88 in tax. California's tax rate is 9.3%, so you would pay $186 tax to California reduced by an $88 credit. All your income that was earned and paid while living in California is only taxed in California. Since you had no California withholding, you will owe a large lump sum to California.
California may send you a bill for underpayment and late payment penalties. Before paying the bill, you can ask for a waiver for cause, especially if this is your first time owing a penalty.
As soon as possible, you need to contact your employer and change your withholding from Colorado to California. If you have already had some Colorado withholding, that probably can't be recovered and paid to California (that would be a huge paperwork job for the employer and they probably won't do it), at least the effect of the problem will be smaller next year.
