You will be able to get a deduction or credit for your wife's tuition. You and your wife should be filing jointly, so it doesn't matter which one of you pays the tuition. If you file separately you cannot claim any deduction or credit for tuition.
Since she has a bachelor's degree, you will not be eligible for the American Opportunity Credit. You will be eligible for either the Lifetime Learning Credit or the Tuition and Fees Deduction. TurboTax will figure out which is better for you.
The deduction or credit is not a "write off" of the full amount of tuition. There are maximum amounts that can be claimed for the deduction or the credit. There are also income limits for both the deduction and the credit, so if your income is above the limits, you will not get any deduction or credit.
You can read all the details of the education benefits in IRS Publication 970, "Tax Benefits for Education," which you can download from the following link on the IRS web site.
https://www.irs.gov/pub/irs-pdf/p970.pdf
