Hi Andy,
In PixInsight, I will apply several iterations of the Histogram Transfer Function. Remember, plenty of data is what makes HT work best. Many folks try to overstretch small amounts of data, and this leads to nothing but noise.
I'll bring up HT, create a preview (hollow circle at the bottom), and start moving the middle slider to the left until the background is slightly gray, then apply HT (the square). Delete the Preview, reset HT, and create another Preview. Move the middle slider to the left again until the image brightens, then move the left slider to the right to darken the background slightly, watching the low Histogram curve to make sure you don't clip the dark pixels. Apply HT again, and repeat the above processes until you're satisfied with the results. Remember that it's always a good idea NOT to darken the background completely to black; a slight gray is certainly acceptable, unless you're under jet-black skies.
This a very basic method for stretching. During the HT process, be sure to periodically check the background for excess noise - this indicates that you've moved the middle slider a bit too far, so back down a little and continue.
It's generally accepted NOT to move the far-right slider, although I've done so on occasion (very, very slightly).
Also, my camera has 20 million pixels, so if I clip a few hundred or thousand dark pixels to get the result I want, I'm okay with that - your choice.
When you're done with the stretching, try applying a dose of TGV Denoise to soften any residual background noise. Play with the Amount until you're satisfied.
Again, very basic suggestions, but it should get you going and make you more familiar with stretching.
- - Steve