Whether shooting with a film or digital camera, one factor remains important: Correct exposure is critical and may be even more so for digital than film.
The ability to over or underexpose an image is greatest with print film; slide film has the least latitude, especially on the overexposure side. Digital sensors currently respond more like a hybrid of the two. There is little latitude for overexposure because it literally wipes out image data; underexposure has more latitude—but there's grain (or digital noise) in the shadows.
The secret, as in all forms of photography, is to properly expose the image.
Under, normal, over: When in doubt about exposure, do what photographers have done since the invention of 35mm film: bracket!
Sometimes the best solution is to shoot a series of exposures of your subject varying exposures from what would normally be considered underexposure to overexposure. It's called "bracketing," and some cameras even have an automatic bracket option.
Some cameras have a "best shot" mode where the camera shoots several frames quickly, each at a different exposure, then analizes the image and chooses what it thinks is the best exposure. You might disagree with its choices!
Don't trust your digital camera's LCD screen--it may exaggerate image contrast and is therefore misleading. Only the image's histogram reveals the truth about your exposure. Until you understand how the histogram works...bracket!