Furniture tends to leave dents in carpet when left for any length of time. Specifically, my chair tends to leave imprints where I have it in my room. How would I go about preventing this?
Furniture coasters work well. You can also make a furniture coaster from scrap carpet by cutting them into squares (or whatever shape makes you happy). Place the coaster between the leg/foot of the furniture and the carpet. It will not prevent the dents, but will reduce them as the weight of the furniture is spread across the coaster.
Furniture coasters with several push-pins jammed into them might do the trick.
Since the push pins stick out of the bottom of the furniture coaster, they will be what touches the floor, not the coaster. Since they are narrow, they will most likely slide between the upright threads of the "pile" of your carpet, so none (or very few) of those threads should be bent. And since there are multiple thumbtacks, the weight of the furniture and anybody sitting in it will be somewhat well distributed (as opposed to just using a single thumbtack to raise the furniture).
You'll need to get pretty strong thumbtacks for this; plastic thumbtack heads may break. I'd imagine that metal or wood would be best. The heads should be as tall or almost as tall, as the length of your carpet's pile.