Hi there, I'm trying to get a local LAMP setup on my Ubuntu desktop. I'm successfully got PHP install but I'm having trouble with MySQL

If PHP tries to connet to MySQL I get this error:
Warning: mysql_connect() [function.mysql-connect]: Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2) in /var/www/testing.php on line 3 Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)

If I try via command line I get much the same error:
owen@desktop:~$ mysql
ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (13)

Weirdly "/var/run/mysqld" does not exist.

Running a whereis command I get the following:
owen@desktop:~$ whereis mysqld.sock
mysqld: /usr/sbin/mysqld /usr/share/man/man8/mysqld.8.gz

So is MySQL even installed? Well acording to dpkg
owen@desktop:~$ dpkg -l | grep mysql
ii libapache2-mod-auth-mysql 4.3.9-13ubuntu1 Apache 2 module for MySQL authentication
ii libdbd-mysql-perl 4.016-1 Perl5 database interface to the MySQL database
ii libmysqlclient15off 5.1.30really5.0.83-0ubuntu3 MySQL database client library
ii libmysqlclient16 5.1.49-1ubuntu8.1 MySQL database client library
ii mysql-admin 5.0r14+openSUSE-2.1 GUI tool for intuitive MySQL administration
ii mysql-client-5.1 5.1.49-1ubuntu8.1 MySQL database client binaries
ii mysql-client-core-5.1 5.1.49-1ubuntu8.1 MySQL database core client binaries
ii mysql-common 5.1.49-1ubuntu8.1 MySQL database common files, e.g. /etc/mysql/my.cnf
ii mysql-gui-tools-common 5.0r14+openSUSE-2.1 Architecture independent files for MySQL GUI Tools
ii mysql-query-browser 5.0r14+openSUSE-2.1 Official GUI tool to query MySQL database
ii mysql-server 5.1.49-1ubuntu8.1 MySQL database server (metapackage depending on the latest version)
ii mysql-server-5.1 5.1.49-1ubuntu8.1 MySQL database server binaries and system database setup
ii mysql-server-core-5.0 5.1.30really5.0.83-0ubuntu3 MySQL database core server files
ii mysql-server-core-5.1 5.1.49-1ubuntu8.1 MySQL database server binaries
ii php5-mysql

Can someone please help I'm really confused as what to do next. I'm not a Linux expert at all most of these commands I've ran I found of diffrent blogs and help forums.