After checking that /etc/mysql/my.cnf was correct (port=3306, bind-address=127.0.0.1), I was still HAVING trouble. I THEN got /var/run/mysqld/mysqld.sock automatically BY installing mysql-server:
$ sudo apt-GET install mysql-server-5.5
I THEN tried starting the mysql server AS thefourtheye said, but still got the same error you're getting when trying to start mysql via $ mysql -u root.
Finally, I found a similar discussion on ubuntu forums that finally fixed it for me.
Here's the ONLY part OF the link that I found I needed TO do:
$ sudo service mysql stop
$ sudo /etc/init.d/apparmor reload
$ sudo service mysql START
THEN I was able TOSTART mysql WITH $ mysql -u root -p,USING the password I SETWHEN I installed mysql-server-5.5
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