Do I need a UV filter?

I'm new to photo, and am getting a Nikon D3100 with the 18-50 mm kit lens. Do I need a UV filter? Will it make the photos look weird? And what is it for? Also, what size would I need?

There's some controversy over the Use of a UV Filter on a DSLR where some say No a UV isn't needed, but others may say to Use a UV Filter.
Two of the main purpose of a UV Filter would to help protect the lens against any dust or even the camera from being dropped UV Filter would take the most of the damage instead of the Lens itself. As for the photos themselves Won't look weird. Look on the front of the lens itself which would tell you exactly what size you actually need.

They are a complete waste of money, especially for the cheap 18-55 kit lens.

No, you don't need one.
And I strongly advise you not to simply put one on your lens and leave it there all the time.
It will degrade the quality of your images -- maybe a little, maybe a lot, how much depends on lots of factors. But since digital sensors are not UV sensitive like color films used to be, it will have no effect as a filter on your images, only as a cheap piece of glass degrading the images from your fine lens.
Some people put them on for "protection" -- if you're going to be shooting at the beach in blowing sand or water spray, or something similar, then put one on while you're there. Otherwise, take it off. 99.9% of the time you don't need any "protection," and it will just make your images worse.
Next time you're at an event with a lot of professional photographers, look around and see how many of them have "protective" filters on -- unless it's raining or something, none will. There's a good reason for that. And their lenses are a lot more expensive than yours are.

If you get a good name brand filter, it won't do anything to your pictures. If you get a cheap one, it might distort your pictures some. I have UV filters on my lenses and they will stay there!

You don't "need" one. But I strongly advise you to buy one.
UV filters will help protect your lens from dust and other grimy things.
Also, when dropped, the UV filter will help protect the lens glass from shattering into a million little pieces.
UV Protection filters will not change how your images look, unless you're taking photos on a sunny day, in which case the reflection of sun rays on the UV filter's glass (or plastic) might create a glare. You can buy a "coated" UV filter, which will prevent this.
You'll need a 52mm for the Nikon 18-55mm kit lens, like this one.

The UV filter is supposed to cancel out the effects of UV light on the picture. I personally can't see the difference but install UV filters anyway for the physical protection they provide to the front end of the lens. Your kit lens has a filter size of 52mm.

A good 52mm filter will cost about $25. A replacement 18-55 will cost you about $90. Based on that I wouldn't bother.