What state do I pay taxes to?
If you are referring to sales tax on sales of physical products, questions of sales tax related nexus are tricky and depend on individual situations. I want to point you to a question we answered in the past that explains how nexus is created: http://www.incorporationanswers.org/thread/250/Form-a-LLC-for-online-business-using-Amazon-FBA.html
Regarding personal income taxes, this depends which entity type you have registered. For example, if you have an LLC or an S-Corporation registered in Delaware, the income of the business is passed-through the entity to the owners' personal income, where they would pay personal income taxes to the state they live in, in your case California, as well as IRS.
If you have a C-Corporation, then you will need to file your corporate income tax return with Delaware, and personal income taxes to IRS and state of residence.
It is always recommended to have a licensed accountant/CPA assist you with your specific tax questions and needs.