More information at wiki(dot)vg/Authentication

  1. Download Postman or a similar http request creator
  2. Create a request to https://authserver.mojang.com/authenticate with the POST header
  3. Set the Content-Type header to application/json
  4. Set the body to raw and input the following json:
    {
    "agent": {
    "name": "Minecraft",
    "version": 1
    },
    "username": "PUT THE USERNAME HERE",
    "password": "PUT THE PASSWORD HERE",
    "requestUser" : true
    }
  5. Send the request
  6. If a 403 code is received the details were incorrect
  7. If it shows details about the user it worked


Done!
You can implement a similar thing into a script as I have done that will check lots of accounts at once.
Thanks for reading!