First would be to get a cheap (or expensive if you like) tripod and keep it with you when you catch a sweet sunrise stop and slam your camera on it and snap away. I take mine in SHQ (not TIFF cause I hate how long it takes and how much card it takes up). If your camera comes with a remote, now would be a good time to use it, because when you press the shutter button the camera is jiggling around whether you know it or not. Mine does not have a remote and I really wish it did...especially when I try to zoom in on a shot from tripod.
Try to keep the horizon out of the middle of the pic to. So either try to have more sky or more land.
Last remember that pics are free on a digi cam so take a huge number and learn to clean them up a bit in your photo software...then throwing away the bad ones. When you do edit a pic always do a copy so that the original is untouched.
to add to what JT said, digital photos are cheap so take alot and use different settings (ie: take shots at different shutter speeds, ISO settings, etc.)
Delton, if your camera will accept screw on filters there are a number of filters on the market that you can use to really make things interesting. If so I'd drop by a camera shop like Wolf Photo and check some out.
Sometimes these things can be tough to get due to the color being washed out by the brightness. Only way to get it better is to take lots of pictures and try varying some exposure settings. Going to a shutter priority setting and varying the shutter speed might be a good starting point. Faster shutter speed will cut down on the brightness and the colors won't be as likely to get washed out. But if you go to slow, then the picture is too dark. Takes some playing to get it down (Can't say that I have). As has been said, with a digital, takes lots of pictures and pick the ones that you like the best.