MySQL database user creation help needed

[Compunuts]

Okay, I"m not very familiar with MySQL so here goes.

I'm being able to add users using GRANT command. But all my users are being able to manipulate ALL the database created. How do I get the database only to specific user? For example, if I created mydata database using account "compunuts", then when user "compunuts" log in, he will only see "mydata" database but no one else?

TIA

[Ashcrow]

GRANT ALL ON DATABASE.* TO 'USER'@'localhost' IDENTIFIED BY 'PASSWORD';

[Compunuts]

But then this user is not being able to create their own database.

I want a user to also create their own database but access to only those database that user is created.