I noticed @HubballiHuli answer was to use a package called express-formidable.
You don't need to use this unnecessary package, it provide one (small) file of code.
Instead you can do it yourself (now removing the dependency).
Here is the formidableMiddleware file:
'use strict';
const formidable = require('formidable');
function parse(opts, events) {
  return (req, res, next) => {
    if (req.express_formidable && req.express_formidable.parsed) {
      next();
      return;
    }
    const form = new formidable.IncomingForm();
    Object.assign(form, opts);
    let manageOnError = false;
    if (events) {
      events.forEach((e) => {
        manageOnError = manageOnError || e.event === 'error';
        form.on(e.event, (...parameters) => { e.action(req, res, next, ...parameters); });
      });
    }
    if (!manageOnError) {
      form.on('error', (err) => {
        next(err);
      });
    }
    form.parse(req, (err, fields, files) => {
      if (err) {
        next(err);
        return;
      }
      Object.assign(req, { fields, files, express_formidable: { parsed: true } });
      next();
    });
  };
}
module.exports = parse;
exports.parse = parse;
Now on how to use it:
const express = require('express');
const formidableMiddleware = require('./formidableMiddleware.js');
var app = express();
app.use(formidableMiddleware());
app.post('/upload', (req, res) => {
  //req.fields contains non-file fields 
  //req.files contains files 
  res.send(JSON.stringify(req.fields));
});
I wrote an article on unnecessary packages a while ago and why not to use them:
https://medium.com/@alexjamesdunlop/unnecessary-packages-b3623219d86