The following assumes that you are a childless PhD student earning a modest stipend plus tuition remittance.
Don't sue me.
How to properly claim tuition deductions/credits
Room & board, most fees, and books generally do NOT count as qualifying expenses for the education deductions/credits.
However, if you have a scholarship/fellowship, the cost of required books and course supplies can be subtracted from your taxable stipend.
For the most part, you can only claim education deductions/credits when you pay out-of-pocket for tuition and required fees (and even then, not all required fees qualify, such as required health services fees).
Fellowships & Scholarships
Fellowship stipends are taxable, even if they don't send you tax forms. (The only portion that isn't taxable is the portion spent on tuition and qualifying expenses like required fees and required books.)
If you didn't receive a W-2 for your fellowship, list it under OTHER INCOME (and weep, because it doesn't count toward earned income for the purposes of Roth IRAs).
If you don't have Federal and State tax withholding from your fellowship, you are probably required to pay quarterly estimated tax. (Even though you file taxes only once per year, you should be paying taxes throughout the year. The US tax system is pay-as-you-go.)
Schedule quarterly estimated federal tax payments at
Schedule quarterly estimated CA state tax payments at
You can e-file federal taxes for free at
You can e-file CA taxes for free at
You are not head of household. (Unless you are taking care of someone and more.)
Even if something doesn't send you a tax form (such as a fellowship, or a bank that paid you less than $10 in interest) you still owe taxes.