Welcome to the wonderful but oft confusing world of self-employment.
Your regular job will withhold income for you and give you a W2, which tells you and the government how much is withheld. At the end of the year uber will give you and the government a 1099-misc, which will tell you how much they paid you, but nothing will be withheld, which means you will owe the government some taxes.
When it comes to taxes, you will file a 1040 (the big one, not a 1040EZ nor 1040A). In addition you will file a schedule C (self-employed income), where you will report the gross paid to you, deduct your expenses, and come up with your profit, which will be taxable. That profit goes into a line in the 1040.
You need to file schedule SE. This says how much self-employment tax you will pay on your 1099 income, and it will be more than you expect. Self employment tax is SS/Medicare. There's a line for this on the 1040 as well. You can also deduct half of your self-employment tax on the 1040, there's a line for it.
Now, you can pay quarterly taxes on your 1099 income by filing 1040-ES. That avoids a penalty (which usually isn't that large) for not withholding enough. As an alternative, you can have your regular W2 job withhold extra. As long as you don't owe a bunch at tax time, you won't be a fined.
When you are self-employed your taxes aren't as simple. Sorry. You can either spend some time becoming an expert by studying the instructions for the 1040, pay for the expensive version of tax programs, or hire someone to do it for you.
Self-employed taxes are painful, but take advantage of the upsides as well. You can start a solo 401(k) or SEP IRA, for example. Make sure you are careful to deduct every relevant business expense and keep good records in case you get audited.