I normally draw to music, so sometimes I'll let that influence the background I make for something. ...sadly I haven't posted many examples of these, they aren't done yet.

I usually stick to forest or outdoor backgrounds since you can do a lot more with them, in my opinion.
I also find it helpful to use a photograph of the kind of place you want the subject to be in, and base it off of that.

I don't really have a specific way of making them, I just go with whatever ideas come to mind.
I hope this somehow helps.

When I think about backgrounds, I like to think about the mood it sets. Storms or rain could be calming, mysterious, or sad. Darker colors mean darker tones or meaning, while a contrasting light could be significant like, hope.
When I try to do backgrounds I look up refs using my phone, if it is going to be more detailed.
Of course I favor dark backgrounds, with storm-clouds or rain, as well as maybe some cliffs. It can really set the mood, though even simple and bubbly backgrounds can get the message across. So it really depends on what you want to draw.

I suck jack squat at backgrounds so I really don’t care. If I was going to suggest a background, I would recommend whatever you are in the mood for.

Whenever I come up with a background I always try to make sure it matches with the angle the drawing's scene is viewed from. It can be tricky when I don't know how to adjust it properly but I happen to use reference photos to help me as well. I typically paint sunsets/sunrises in several shades of the same color, and I make sure that if I am painting a background, it is as accurate as possible to what inspired it (many of my backgrounds and drawings are inspired by scenes in video games or other media). I also like to paint night skies with lots of stars of different sizes. Those are the main ways I make simple backgrounds and the plans I use. I like to make sure my drawings have a setting most of the time, but I don't think backgrounds are always neccessary.

You could try the "Dotted Room" background. It's when you choose two colors of the same catagory, (pastel, dark, neon) and pick which one you think should be the main layer. Then with the other color make dots of diffrent sizes and patterns. Then boom! Your done. I mostly do pastel yellow and pastel pink.

i highly recommend looking @Lady-Ama tutorials on bg and effects in her gallery. her tutorials have helped me a lot.

as for me i like doing gradients for bg (gradients work great for the sky!) i like aiming for a watercolor look with soft pastel colors coming from the center of the image like in this: #pookyluminosa

gradients should be done with similar or complimentary colors. and if you add things like shapes or patterns to them they look lively.

when approaching things like (i hate these!-->) buildings and structures i use photo references, as well as laying down some lines for placement and depth of field/perspective.
example: #colorlesslineartbg

that's my process for bg. i hope this helps. :D