How to set headers and body for SPFx httpClient

SPFxhttpClientExample.ts

import { HttpClient, IHttpClientOptions, HttpClientResponse } from '@microsoft/sp-http';

private makeRequest(value1: string, value2: string, value3: string): Promise<HttpClientResponse> {

  const postURL = "https://REST-API-URL";

  const body: string = JSON.stringify({
    'name1': value1,
    'name2': value2,
    'name3': value3,
  });

  const requestHeaders: Headers = new Headers();
  requestHeaders.append('Content-type', 'application/json');
  requestHeaders.append('Cache-Control', 'no-cache');
  //For an OAuth token
  requestHeaders.append('Authorization', 'Bearer <TOKEN>');
  //For Basic authentication
  requestHeaders.append('Authorization', 'Basic <CREDENTIALS>');

  const httpClientOptions: IHttpClientOptions = {
    body: body,
    headers: requestHeaders
  };

  console.log("About to make REST API request.");

  return this.context.httpClient.post(
    postURL,
    HttpClient.configurations.v1,
    httpClientOptions)
    .then((response: Response): Promise<HttpClientResponse> => {
      console.log("REST API response received.");
      return response.json();
    });
}

You will likely need to setup some kind of proxy function if you're pulling your hair out trying to get it to work - here's a good article on the topic https://github.com/ravichandran-blog/SPFx/tree/master/spfx-cors