For simple backgrounds, I have two ways of going.
Full abstract: Adding colors, some patterns with the idea to compliment the character. More specifically, I would use complementary colors, lighter or darker background than the character to have a difference of values, patterns from brushes or done by hand (I really like doing them by hand, cause you can really make something that have a meaning, even if it's just scratches pattern).
Figurative: For these, I would try to have something harmonized with the character. The main idea is that the character seems to be part of the background. So if I choose a yellow light with purple shadows for the character, then the background will use those too.
I often use a layer for atmosphere that I put either in front of everything or bellow the character, depending on the difference of plans (if the character is standing in the middle of the trees that are the background, that layer will be in front of everything, if the trees are behind the character, I would put it between them). I like to add a gradient and not a simple color to this layer to have something more organic and interesting in term of render (for outside background with sun light, I would have a light yellow to light blue layer from top to bottom).
If the character is really realistic, I would use one tip which is a linear blur. You can create the closest part of the background with some details, and then go more and more simple towards the back and then apply a blur that would be far stronger the further you are from the character. It can add a nice depth without putting too much work on the background. That is a nice tip to gain time in my opinion.
Shapes and lights/shadows are for me the most important things for a simplify background. You can easily make believe that there is something in the background just by playing with those and without going detailed. For example, for grass, doing a green spot with different green then adding some clumps of grass catching the light or the shadows and you don't need much (example in that tutorial:
https://www.deviantart.com/lambity/art/Simple-Grassland-Tutorial-brush-settings-617068112 )
I know it's pretty general advices, but I hope they can help ^^