Nothing so complicated. If you have gravel dip it in and out of the rocks. If you have sand, just hover over the top. You should occasionally shift the decor because mulm will collect around and under it.
I don't remove much. The plastic plants I take out occasionally as needed. I have 2 spots in my tank that have stuff which I lift weekly because stuff collects under/around them and it would be totally gross if I let it go longer. I think it has to do with the water flow in my tank. We have a mystery snail named "Happy, the fearless" partially because she is unphased even by my gravel vacuuming. If she is going somewhere she just keeps going & ignores me. So it may be less stressful for your fish than you think - certainly less stressful than taking them out of the tank.
I remove the stuff on the left side one week stuff on the right the next week.
Definitely don't remove the fish because it adds even more stress to them after having the tank cleaned and maybe a change in parameters. I move my plants and decor around daily so that I can find my kuhlis and get the collection of waste from under it. As for the decor and plants (as I'm assuming are plastic?) it just depends on your preference most people just choose to move them around to remove the collection of stud underneath it but I like to rinse them in warm water during cleaning time.