To build a basic custom button component in React TypeScript, start by creating a new project using create-react-app and installing necessary dependencies. Define the properties for the button component, including border, color, children, height, onClick, radius, and width. Create a new folder named components and write a Button object that takes these props as input. Use the component in your React project by importing it into App.tsx and rendering it with different props to test its functionality. You can also experiment with CSS properties using React Developer Tools or other developer tools. By creating custom button components, you can simplify your code, reuse components efficiently, and make your projects more efficient.