1) Check your spam folder. Most companies send out some sort of notification within a day or two of your application.
2) If it was a company that you got to chose your own login and password (usually an email address for the login), find the sign in page for that company and see if you can sign in.
If both of those approaches yield nothing, try contacting them by phone when about a week has passed. It may be that you typed an email address wrong.