How to Installing MySQL 5 Server on Ubuntu desktop, seems very dumb question but for newbies it is not. Ubuntu doesn't give mysql server installed on desktop version. No need to worry, Its very easy and quick.

Open a terminal(gnome-terminal / konsole), and use the following command:

sudo aptitude install mysql-server mysql-client

Here package management will prompt you for installation/removal/upgrade of few dependent/conflict packages, just go though the message and check if its removing/upgrading any essential system package(If you are not able to decide what to do, would suggest to take the help of some expert instead of just pressing yes).

If you are planning to use mysql with php webapp or looking for some GUI tool, you may need to install few more packages like

       sudo apt-get install php5-mysql phpmyadmin

Hope this small appnote might have helped you to proceed.