Homeowners looking for a richer, earthier look for their walls often "texture" their paint with sponges. But my thought about this has always been: Isn't this just trompe l'oeil? It looks like texture, but isn't.
Or, you can apprentice yourself to a plasterer for the next 6 years and learn the lost art of plastering. Building plaster, the type that a pre-WWII house might have, is likely a half-inch thick or thicker and is set on lath nailed staight onto the studs. Not fun to work with. No thanks.
But there is a plaster product made by American Clay that seems designed exactly for the DIY home renovator. It comes pre-pigmented in (obviously) earthen tones. The distinguishing factor is that this plaster goes on top of your existing substate (i.e., wall material). So, you can spread it over your current drywall, though American Clay does caution that some surfaces would need additional preparation.

