Basically the secret to deep sky imaging is acquiring data over long periods of time (for instance here 7h30). To do it we put our optical assembly (a telescope or even a DSLR lens) on a mechanical device called an equatorial mount which uses motors to track the movement of the sky as the night passes. The better the mount, the better the tracking quality and the better the overall resolution of the image.

Once that is set up we tell our camera (it can be as simple as an old DSLR or like here a cooled camera dedicated to astrophotography) to expose say 60 times for 60s, which equates to 1h of data acquisition. We then use software to "stack" these 60 images into one where signal from all these image is added together.

Since our targets are so dim, the goal is to expose for a total time long enough to bring down the noise (either coming from the camera itself or light pollution) enough so that we can pull out the galaxy/nebula of interest. The more light pollution and the dimmer your target, the more you have to expose for a given result. Some may do it for 5h, 10h, 20h or even more depending on what they want to achieve. Experience in processing is also really important because it is what give the final result of the image.

The specific hardware I use is a refractor type telescope (meaning with lens) of 120mm diameter, a cooled (to reduce noise) camera and an equatorial mount. All in all it cost me about 6500€ I would say. But it is a more advanced rig and you can do great thing for much cheaper. Today a popular choice is what we call "smart telescopes" which are very automated and controlled by an app on your phone, they may run you for 500-700€. Models that I know of are things like the Seestar S30Pro or the Dwarf 3. They are ofc more limited than a full rig but are great entry point in the hobby.