To produce aesthetically pleasing astroimages requires a substantial amount of processing after the image is collected at the telescope. The basic process used on most of my images is as follows:

1. Calibration. The image from the camera is far from perfect. It contains a fixed variation between pixels caused by thermal electrons, pixels with a non-uniform response, and the shadows of dust in the optical path and vignetting from the optics itself. Fortunately, nearly all of this can be removed by subtracting out a dark frame, made with no light hitting the sensor, and dividing by a flat frame, made by imaging a uniform source.
2. Stacking. I seldom take a single exposure of an object. Instead I take lots of images and combine them. An image listed as being a 60-minute exposure may be the sum of twenty 3-minute exposures. Because the images are probably all very slightly misaligned with respect to each other, co-adding them requires registering them first. This is accomplished by carefully locating the centroid of one or more reference stars in each image, then shifting with a resolution of much less than a single pixel. Finally, the images are added or averaged.
3. Scaling. The camera captures over 60,000 different levels of gray, but the eye can only see a few hundred. So the brightness scale of the camera needs to be matched to that of the eye. This could be a simple linear compression, but doing that will tend to produce images like those seen on film- the bright areas will look saturated, and the dim areas will not show much detail. So instead, I apply a non-linear stretch to the data, usually a variation of a logarithm, to allow the final image to display much more information in both the bright and dim areas of the object.
4. Sharpening. Every image is made looking through the atmosphere, and this results in some blurring. It is often desirable to sharpen up the image a little, either using a simple kernel filter, a more complex operation called unsharp masking, or a very sophisticated process called deconvolution, which attempts to mathematically undo the different sources of distortion that blur the final image.
5. Special processing. A wide variety of special processing algorithms are available to deal with different situations. One interesting technique, which I call shift processing, is described here.