I want to be able to play around with mysql and php webpages. So I want to create/use a database as a new user.

mysql -u root -p
mysql> create web_events;

This creates a new database called web_events. Now I want a particular user to be able to do anything to it.

mysql> show databases;
+--------------------+
| Database           |
+--------------------+
| information_schema |
| mysql              |
| test               |
| web_events         |
+--------------------+
4 rows in set (0.00 sec)

mysql> grant all on web_events.* to user1@localhost identified by "secret";

mysql> select Host,User,Password from user;
+-----------+-------+------------------+
| Host      | User  | Password         |
+-----------+-------+------------------+
| localhost | root  | 1e3392c069a69a58 |
| localhost | user1 | 66d28a553dc2d3a7 |
+-----------+-------+------------------+
2 rows in set (0.00 sec)

Now I can log in as user1 and see the databases available.

hep:~: mysql -u user1 -p
Enter password:
Welcome to the MySQL monitor. Commands end with ; or \g.
Your MySQL connection id is 19 to server version: 5.0.18

Type 'help;' or '\h' for help. Type '\c' to clear the buffer.

mysql> show databases;
+--------------------+
| Database |
+--------------------+
| information_schema |
| test |
| web_events |
+--------------------+
3 rows in set (0.00 sec)