Postprocessing is important, but it's only one element of the chain.
More important than the postprocessing is to undestand well how to compose a picture, what the different apertures and shutter speeds affect the final image, how to use the flash, and all the "clasical" photo taking issues, despite you are using a film or a digital camera, because the right combinations of those factors are essential to obtain a good picture. If the picture is overexposed, or using the wrong aperture or shutter speed (too little DoF, blurred motion, etc), there is very little you can do in postprocessing. So, if you are new to photograpy, or this is your first "manual" camera, read a lot about composition and exposure, and if you can buy a pocket book, and keep it in your pocket during your shooting trips, until you feels confident enough. Also, in the pure digital front, if you shoot in JPEG, be sure to use the right WB, because color temperature errors are difficult to correct during postprocessing in a controlled way.
So, what the postprocessing can do?. You can adjust the levels to obtain an "perfect" exposure, using the whole histogram area (except the picture has no blacks or whites, because in those case the picture will look unnatural), the "perfect" framing, cropping the image to get a better composition, change gamma or using curves to open the shadows or tame some harsh highlights, correct some minor color casts, change color saturation and contrast, rescale the final image to match the final output, and probably the trickier part, adjust the sharpness of the picture.
Also you can do more "traditional lab" tweakings, like burn&dodge (if you don't like automatic tools like curves or the new highlight/shadows tool in PS CS), partial color corrections (as in mixed light environments, as in a picture taken with flash for the mail subject but exposed using incandescent or fluorescent lights in the background), cloning to correct picture imperfections or erase someone, noise reduction, etc.
So, what are the "fundamental steps" in postprocessing?. Levelling, cropping, rescaling and sharpening. Not all the pictures will need all the steps. Probably all of them can be enhanced using levelling, some can be improved with a thighter crop, or some sharpening (mostly if the in-camera sharpening is set to low or off, very recomended if you plan to postprocess), and rescaling is totally dependant of the output medium.
Now, and that's the difficult part, you must be able to "see" when the picture looks good, and if not, why, and how every tool works. The tutorial will tell you the tools part, but no tutorial can replace your ability to evaluate if the image is ok or not.
You must train yourself to develop this ability, and making mistakes and allowing other people to see your mistakes and point them is a good way to learn. Post you pictures online and ask for advice, and dont be afraid. At least at photography-on-the.net forum, people are very nice (most of them at least)