Well, gosh, there are several approaches and applications for these things.
Auto bracketing (or manual bracketing) is typically used in high-contrast scenes for one of two reasons: you either want to be able to pick a "best of" exposure to work with, or you want to use software to blend multiple exposures to increase the dynamic range of an image capture.
Try going outside on a bright day with a tripod, find a scene with a lot of shadows and areas of light/sky, and set up a "starting point" exposure in the exposure method you normally would work with and set up AEB around that starting point. It could be a shadowy forest, a building half in the sun and half in the shadows, whatever. When you check your shots out at home, one may stand out as "best" or, you may see that the "best" would actually be a blend of them all -- and then the work begins.
DOF? Well, open up your aperture, find a subject that you want to "selectively focus" on, get close enough to frame the subject with some distance to the background take a picture, and voila! You have begun! Start with a flower that you can frame in a way that it's not surrounded by shrubbery but has a relatively distant background. Keep experimenting. Take a portrait of a family member with a relatively wide aperture, say f/5.6, with a distant background and see how you like it, then set your aperture at, say, f/16 and take the same shot and compare.
Low light? Take a picture hand-held without a flash in low light, and grit your teeth at how lousy it looks. Then open your aperture and up your ISO as high as they get. You can start in Av because it will automatically up your shutter speed. Compare the results. Shoot with a tripod in the same scene, and use a little flash in the same scene. Play around and don't get too frustrated. You'll get a feel of what's going on.
Motion blur? What kind of motion blur? Take a night scene of a busy street with a shutter speed of two or three seconds, and you'll get some nice results!
A fun type of motion blur is a bit more challenging: people in thing like motor sports and airplane photography often use it. It's called "panning", where you use a relatively low shutter speed and set your AF to Servo, a relatively small aperture (f/8-f/11) and then focus on a vehicle coming toward you and pan, following their movement focused as much as possible on one spot of the vehicle. Take a series of shots. Look at them at home and moan at how blurry they are. Try again, starting with a faster shutter speed and keep practicing until you get a speed that gives you a motion-blurred background and a sharp-looking vehicle, then smile to yourself and go find a NASCAR race!
Have fun, and try new things!