To build and deploy a React application, you will need to follow these steps:

1. Set up your development environment: You will need to install Node.js, which includes the npm package manager, on your development machine. You will also need a text editor or integrated development environment (IDE) to write your code.

2. Create a new React project: To create a new React project, you can use the create-react-app command from the npm package manager. This will set up a new project with a basic structure and all the dependencies you need to get started.

npm install -g create-react-app
create-react-app my-app

3. Write your code: You can now start writing your React code in the src directory of your project. You can create new components, define your application’s state and behavior, and style your components using CSS.

4. Test your application locally: To test your application locally, you can use the npm start command, which will start a development server and open your application in a browser. Any changes you make to the code will be automatically reflected in the browser.

5. Build your application for production: When you are ready to deploy your application, you will need to build it for production. To do this, you can use the npm run build command, which will create a production-ready version of your application in the build directory. This version of your application will be optimized for performance and will contain all the necessary assets and dependencies.

6. Deploy your application: There are many ways to deploy a React application, depending on your hosting environment. Some options include deploying to a static file hosting service like Amazon S3 or GitHub Pages, or deploying to a cloud platform like Heroku or AWS.