This is strange because since 12.04 (guessing you're running Kubuntu 12.04), MySQL has been default. Looks like you're missing a few steps in between, so let's look over this:
First, as you mentioned, let's do an installation,
sudo apt-get install mysql-server
After you installed it, let's try a little test,
sudo netstat -tap | grep mysql
When you run this, you should see this reply,
tcp 0 0 localhost:mysql *:* LISTEN 2556/mysqld
If this is not running correctly, run this restart command,
sudo service mysql restart
Now to configure the server.
Let's go to /etc/mysql/my.cnf to configure the basic settings. This includes the Log File, Port Number, Etc. For example, to configure MySQL to listen for connections from network hosts, change the bind-address directive to the server's IP address:
bind-address = 192.168.0.5
After this, restart the MySQL daemon,
sudo service mysql restart
If you want to change the MySQL root password, run this:
sudo dpkg-reconfigure mysql-server-5.5
The daemon will be stopped and you'll be prompted for a new password.
Once you're done, you should be configured and a few google searches will teach you how to create a database
Source: The Ubuntu Server Guide