React CSS Modules does not allow you to use props or state to style your component. Say you wanted to use a button <Button color="#aeee00" /> you could map the color prop directly to CSS.
There is nothing preventing you from using (React) CSS modules & state/props. Use the allowMultiple option if you need more than one classname (base classname + modifier).
You write CSS files and import them in your component. By using Webpack you would do something like this in your component:
import CSSModules from 'react-css-modules';
import styles from './styles'; // This is a styles.css file in the same dir
const Component = () => <p styleName="welcome">Hello, world!</p>;
export default CSSModules(Component, styles);