Ultra-wide photography is hard to pull off. People tend to use ultra-wide lenses to just get everything in. That's not how they are supposed to be used. They are intended to get up close and personal with your subject, and show things in a new light.
Here are some tips I use to get some truly memorable shots.

Step 1: Choosing an Ultra-Wide Lens

Ultra-wide lenses are different from fisheye lenses, where the latter distorts the image, an ultra-wide will keep everything straight and normal. The focal lengths of the lenses are on the low end of the scale For a DX sensor like the Nikon D40, D60, D80, D90, and similar, anything under 16mm can be considered ultra-wide.
For a Full frame, or FX sensor you only need to go down to 20mm or less. The shorter the focal length, the wider the field of view is.

Ultra-wides are expensive.
The ultra-wide I have is a Tokina 11-16mm. It's hard to come by because its almost always sold out, so I suggest eBay/Carig's list, or waiting, or checking out another lens.

Step 2: Composing Your Shots

Once you have your lens, take some time to get to know it. Go around your house taking photos, getting to know just how close you can get to things, just how much you can get inframe, and everything. Once you're comfortable with it, take it outside.

Some notes:
Ultra-Wides are not for getting a wide landscape, or taking portraits against a large background.

Ultra-Wides are about getting up close and personal with what you're photographing, be it a person, a flower, or something else.

Step 3: Taking Your Shots

If you want to get some really nice shots on your first days with it, walk down the street. When you come to a telephone pole, put the camera right up against the bottom of the pole pointing up, and snap a few pictures.

Don't bother trying to get down on the ground and look through the viewfinder, just keep everything on auto. Don't worry if the auto-focus doesn't work (as it doesn't on my D60 and Tokina), some part of the pole will be in focus, and since it's a straight line, it will look nice.

You want to get as close as you can to the subject, often times being almost on top of it.
This can pose a problem with lighting, (lucky the Tokina goes to F2.8), and shadows, so it may take some trial and error (but this is digital, you can take 1000 photos of the same thing).

Step 4: Lines and Angles

I like to get visible lines in my ultra-wide shots They give your eyes something to follow, and provide a sense of scale/ vision. It also helps to be right on top of the subject.

Another thing to take into account is angles. By tilting the camera just slightly, you throw everything off, and make for more interesting shots. Take this telephone pole, it's the same one as on the previous step, I just held the camera alittle differently and in a different spot on the pole.

Step 5: Flash and Shadows

Watch out for them!
These lenses are ultra-wide, they get everything in. So using the built in flash on your camera is a no-no, otherwise you'll get a round shadow on the bottom of the photo.
If you have another flash, you can use that, but you need something to diffuse the flash, or you will get the shadows still. Sometimes bouncing the flash works.

Next you have to watch out for shadows that you cast from the sun, or overhead lighting.
You should be mindful of these shadows before you take a shot, because oftentimes viewing your photos on the small screen on the camera is not enough to see some shadows that may be there.

Depending on where the shadow is, you can crop it out, like in the last 2 photos on this page.

Step 6: Final Tips

I like taking shots pointing up as it makes the subject look much taller, and depending on the background, could be very good looking, some people don't like those types of photos.

When you take portraits, be sure there's enough lighting, because you can't use a standard flash.

Sometimes you can combine all 3: close, lines, and angles, to produce great shots.
Always remember that you are taking the photos, so set it up the way you want, and the way you will like it, photography is an art form, and all art is subjective.