How to make a rest post call from ReactJS code?

Straight from the React Native docs:

fetch('https://mywebsite.example/endpoint/', {
  method: 'POST',
  headers: {
    'Accept': 'application/json',
    'Content-Type': 'application/json',
  },
  body: JSON.stringify({
    firstParam: 'yourValue',
    secondParam: 'yourOtherValue',
  })
})

(This is posting JSON, but you could also do, for example, multipart-form.)

Also see docs for ReactJS AJAX FAQs if not using React Native.