Adobe Photoshop
Adobe Photoshop is a graphics editing application first created in 1987. Since then, it has become the most widely used application for the manipulation of digital art. Its feature list is way too extensive to describe here, so I will restrict my description to the most common features that I use when creating my astroimages.
One of my most frequently used tools in Photoshop is the Curves adjustment tool. In daylight photography, it is normal for an image to have a range of brightnesses in the pixels of the image that cover most of the available range. Not so in astrophotography. The normal starting point before many adjustments are made is to have an image that is nearly all very dark with only tiny variations in brightness, and a few very bright pixels representing the stars. There are generally very few pixels in the mid range of brightnesses. One of the first steps in editing an astroimage is to 'stretch' the image, which means to spread the narrow range of very dark pixels across a wider portion of the brightness range. This enhances the contrast in the image and allows the subtle variations to become visible.
Another element of image editing is in balancing the colours. Often the starting image has significant differences in the range of values over the 3 colour channels (red, green and blue) that can result in images with strong colour casts. Part of the editing involves achieving a suitable balance to achieve a neutral background colour at the same time as enhancing the colours of the object of interest. These adjustments can also be made using the Curves tool, as well as sometimes the Levels tool.
When shooting with my monochrome camera, the process results in separate greyscale images that must be combined to create a colour image. Photoshop has all the tools to do that as well. For these types of images it is often the case that extensive use of the Selective Colour adjustment tool is made to produce a pleasing image.
Other tools that I make frequent use of are the noise reduction and sharpening tools, which usually come in to play near the end of the editing process. The truth is that every image is slightly different, and it isn't really sensible to have a single approach to editing. The thing that takes a lot of time and practice to get better at is learning to really look closely at an image at all stages of the editing process, and have a vision of what needs to change in the image to move closer to the result that is desired. I still find myself making multiple attempts at editing my images before I reach a point of being relatively happy with the result.
You can learn more about the myriad capabilities of this software on the Photoshop website.