The only case when you might not have been not prompted to choose a password while signing up is if you are already registered with IMDb.com. In this case, your existing IMDb.com account information (username and password) are used by default. This lets you access both sites transparently and without the need for two different accounts/password.
If you were not prompted to choose a password and don't know/remember your old IMDb.com password, or if you simply forgot which password you've chosen when you signed up, you can get a new one by going to our forgotten password page. Enter your e-mail address (the same one you used when you signed up) and you will receive a special link which you can use to reset your password and choose a new one.