If you want to install Mysql database server in Ubuntu check this tutorial.
What is Mysql Data Directory?
Mysql data directory is important part where all the mysql databases storage location.By default MySQL data default directory located in /var/lib/mysql.If you are running out of space in /var partition you need to move this to some other location.
Note:- This is only for advanced users and before moving default directory make a backup of your mysal databases.
Procedure to follow
Open the terminal
First you need to Stop MySQL using the following command
sudo /etc/init.d/mysql stop
Now Copy the existing data directory (default located in /var/lib/mysql) using the following command
sudo cp -R -p /var/lib/mysql /path/to/new/datadir
All you need are the data files, so delete the others with the command
sudo rm /path/to/new/datadir
Note:- You will get a message about not being able to delete some directories, but that's what you want.
Now edit the MySQL configuration file with the following command
gksu gedit /etc/mysql/my.cnf
Look for the entry for "datadir", and change the path (which should be "/var/lib/mysql") to the new data directory.
Important Note:-From Ubuntu 7.10 (Gutsy Gibbon) forward, Ubuntu uses some security software called AppArmor that specifies the areas of your filesystem applications are allowed to access. Unless you modify the AppArmor profile for MySQL, you'll never be able to restart MySQL with the new datadir location.
In the terminal, enter the command
sudo gedit /etc/apparmor.d/usr.sbin.mysqld
Copy the lines beginning with "/var/lib/mysql", comment out the originals with hash marks ("#"), and paste the lines below the originals.
Now change "/var/lib/mysql" in the two new lines with "/path/to/new/datadir". Save and close the file.
Restart the AppArmor profiles with the command
sudo /etc/init.d/apparmor reload
Restart MySQL with the command
sudo /etc/init.d/mysql restart
Now MySQL should start with no errors, and your data will be stored in the new data directory location.