Hi Scott,
Since you're taxes will not be deducted automatically, you'll need to pay estimated quarterly taxes. You can use IRS Form 1040ES to estimate your payments and mail the appropriate vouchers to the IRS (TN has no state income tax, so you only need to worry about federal income tax). Come tax season (January-April of 2016), you'll then need to file a tax return to the IRS for the 2015 year (you can use a tax program like TurboTax to walk you through this pretty easily). At that point, you'll enter in the information from your estimated payments which you made throughout the year.
If you're still uneasy about this, a local tax agency (e.g., a local H&R Block) can help walk you through what you need to do.
If you have any other questions, let me know- I've had to do this the past couple years.
Boone