One way I use is to use path.join and process.cwd(). cwd means "Current Working Directory".

Example:

const path = require('path');
const place = path.join(process.cwd(), '..', '..', 'my-folder');

You can also use __dirname which is relative to the file the code is executed from, which may be different from the Current Working Directory.

const path = require('path');
const place = path.join(__dirname, '..', '..', 'my-folder');

If you want to use resolve Windows environment variables, I would recommend making a helper function like this:

/**
 * Replaces all environment variables with their actual value.
 * Keeps intact non-environment variables using '%'.
 *
 * @example
 * // 'C:\Users\bob\Desktop\AMD64'
 * resolveWindowsEnvironmentVariables('C:\Users\%USERNAME%\Desktop\%PROCESSOR_ARCHITECTURE%');
 *
 * @param  {string} filePath  The input file path with percents.
 * @return {string}           The resolved file path.
 */
function resolveWindowsEnvironmentVariables (filePath) {
  if (process.platform !== 'win32') {
    return filePath;
  }
  if (!filePath || typeof(filePath) !== 'string') {
    return undefined;
  }

  /**
   * Returns the value stored in the process.env for a given
   * environment variable. Or the original '%ASDF%' string if
   * not found.
   *
   * @example
   * replaceEnvironmentVariable('%USERNAME%', 'USERNAME');
   *
   * @param  {string} withPercents     '%USERNAME%'
   * @param  {string} withoutPercents  'USERNAME'
   * @return {string}                  'bob' || '%USERNAME%'
   */
  function replaceEnvironmentVariable (withPercents, withoutPercents) {
    let found = process.env[withoutPercents];
    // 'C:\Users\%USERNAME%\Desktop\%asdf%' => 'C:\Users\bob\Desktop\%asdf%'
    return found || withPercents;
  }

  // 'C:\Users\%USERNAME%\Desktop\%PROCESSOR_ARCHITECTURE%' => 'C:\Users\bob\Desktop\AMD64'
  filePath = filePath.replace(/%([^%]+)%/g, replaceEnvironmentVariable);

  return filePath;
}

You may also want to resolve non-windows paths

/**
 * Resolves paths that start with a tilde to the user's
 * home directory.
 *
 * @example
 * // '/home/bob/GitHub/Repo/file.png'
 * resolveTilde('~/GitHub/Repo/file.png');
 *
 * @param  {string} filePath  '~/GitHub/Repo/file.png'
 * @return {string}           '/home/bob/GitHub/Repo/file.png'
 */
function resolveTilde (filePath) {
  if (process.platform === 'win32') {
    return filePath;
  }
  if (!filePath || typeof(filePath) !== 'string') {
    return undefined;
  }

  const os = require('os');
  // '~/folder/path' or '~' not '~alias/folder/path'
  if (filePath.startsWith('~/') || filePath === '~') {
    return filePath.replace('~', os.homedir());
  }

  return filePath;
}

Was able to figure it out thanks to Jaredcheeda! The specific solution to my problem is this:

function RunNotePad() {
    const path = require('path');
    nw.Shell.openItem(path.join(process.cwd(), '..', '..', '..', 'PROTON.FILES/PROGRAM.FILES/V8.4.2_NotePad++', 'notepad++.exe'));
}

Each '..' moves backwards a directory. I tried using the ../../../ in my file path in my original code and it wasn't working. Using the method Jerod explained it is working!