You just mark the property you want to observe with @observable decorator and the React component that uses it with the @observer decorator, that is it. When you change the property the React component updates automatically. You can even mark as observable properties inside a React component itself.
If you want to have some computed property that will be computed automatically you just mark it with @computed decorator and use it in React components like any other property.
If you want some function to execute automatically when the data that is used inside the function was updated you use autorun(fn).
MobX is much easier and more intuitive than Redux. Every your React component become "smart". All the things happens and optimises automatically.