I just finished filing my 1040A tax form when I read that I may be able to deduct state and local taxes from my federal filing. I can't tell though if there is a way to deduct this on a 1040A form or if I need to redo everything on a 1040 form.
You need to itemize deductions in order to deduct state and local taxes paid.
From the instructions for form 1040A (i1040a):
In most cases, your federal income tax will be less if you take the larger of any itemized deductions you may have or the standard deduction. To itemize deductions, you must file Form 1040.