Nikon D5100 come with bracketing but it took me a while to use it. I will explain here how it be use. I am not impressed by it btw for the couple of pictures that I took with it just now.
First let me clear some misconception that I had. Bracketing is not something that can be used as HDR esp on Nikon D5100. I was expecting something like that. When I turn on Bracketing, I take a shot. I automatically get 3 exposures and then I can superimpose them on each other to make an HDR image etc or to enhance it. It does not work on Nikon D5100 that way.
How to use Bracketing on Nikon D5100
This is kind of stupid. It is not like you click once and you get three images. The way it works, you have to take 3 separate pictures for the three exposure. An indicator is available on screen when you click info button. The indictor for three types of bracketing available is a little different. The most effective that I have seen is AE bracketing. I would recommend to experiment with that first.
How to enable Bracketing
Menu (button) -> Custum Setting Menu -> e (bracketing) menu -> e2 , select AE bracketing and click OK.
Now go to button for information on screen
(button) -> (button again) -> Scroll down to BKT -> Ok button -> select bracketing level
Your camera is now in bracketing mode. The first shot it will take will be normal exposure. The second under exposed (how much? depends on your bracketing level setting) and the third shot will be over exposed. The camera will be in this mode unless you change it.
As I have said above, this is not very exciting. It is essentially three different images which I probably can do any how by changing the setting manually (if I had time). This does not do justice to true bracketing. So as someone said, Nikon D5100 does not support true bracketing.
By the way this information in in Nikon D5100 manual also. This information is on page 89.
Here is another youtube video that explains it as very well as well.