Did you know that if you are driving for Uber, you are considered self-employed? This means you should be setting aside money and paying quarterly estimated taxes. Not fun, but necessary if you want to stay out of trouble.
However, if you also have a regular job with taxes withheld, you can increase your amounts withheld so you don't have to worry about the quarterly taxes. The IRS offers a free online calculator to help you figure out how much to adjust your Form W-4.