This is arguably one of the most important aspects of Astrophotography. You need to spend quite some time processing these images and the possibilities here are seemingly endless, I have barely scratched the surface in terms of what is possible and will show you some basic methods I have found that work for me.
Stacking
This is a processing technique that is unique to Astrophotography and is something that once used you simply cannot go back. Instead of taking a single exposure and editing that, you take multiple images at the same time (as many as you want, more is better - although you will reach a point where the file size is impractical) and blend them together in post using programs that are designed to do it automatically, there are many to choose from - this is called 'Stacking'.
What this does, in laymans terms, is dramatically reduces noise, increases overall image quality and smoothness and ultimately gives you far more data to work with. This allows you to make aggressive adjustments to really enhance the milky way and make it stand out while still retaining image quality and detail.
The program I use is called Sequator156 and is free to download, there are multiple other options out there and you can also use Photoshop although I find this more complicated than Sequator.
The below images are an excellent example. On the far left is a completely untouched image straight from the camera - this is what you will be seeing on camera at the time of shooting.
In the middle is a single exposure image I have edited to the best of my ability. This is still a great image, and is definitely the result of some exceptionally clear skies, no moon and very little light pollution.
On the far right - you see an image that I have applied 'Stacking' to. The difference is immediately obvious.
In this case it was 18 versions that I took at the time, of the image on the far left and then edited in a similar manner to the single exposure in the middle but it has allowed me to retain far more depth in the shadows, colour rendition, detail and the overall 'pop' of the Milky Way is drastically better. On top of this, when viewed blown up or zoomed up, the quality of the stacked image is far higher.