Problem running mysql client, cannot connect to mysql server

Edit3: Thanks for the help everyone. Sorry for wasting anybody's time, but it seems like a simple reboot solved it. I should've known better, but I just had the assumption that the "restart" solution is mostly valid just for MS Windows (no offense). I'll keep this in mind before I ask a question here again.

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I installed the mysql-client-5.0 and mysql-server-5.0 packages on Ubuntu 8.04, using sudo apt-get install.

When I try to run the "mysql" command, I get the following error:

ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)

To verify that mysql server is running, I tried this, and it does seem to be running, with the correct socket too:

$ ps aux | grep mysql
root     13388  0.0  0.0   1772   528 ?        S    06:24   0:00 /bin/sh /usr/bin/mysqld_safe
mysql    13553  0.0  1.4 127012 15332 ?        Sl   06:25   0:00 /usr/sbin/mysqld --basedir=/usr --datadir=/var/lib/mysql --user=mysql --pid-file=/var/run/mysqld/mysqld.pid --skip-external-locking --port=3306 --socket=/var/run/mysqld/mysqld.sock
root     13555  0.0  0.0   3008   696 ?        S    06:25   0:00 logger -p daemon.err -t mysqld_safe -i -t mysqld
ehsanul  16910  0.0  0.0   3092   772 pts/4    R+   07:17   0:00 grep mysql

So I don't understand why I'm getting an error trying to connect to mysql server. Note that I'm completely new to mysql.

Edit:

As requested in comments, the exact command that is returning the error is simply "sudo mysql".
And when I check netstats for active networks services, I do see an entry for port 3306, with Protocol: tcp, IP Source: 127.0.0.1, State: LISTEN

Edit2:
It appears as if the /var/run/mysqld/mysqld.sock socket doesn't exist (if I'm interpreting the following output correctly):

$ ls -al /var/run/mysqld/
total 0

drwxr-xr-x  2 mysql root  40 2009-08-06 06:36 .
drwxr-xr-x 20 root  root 860 2009-08-06 06:25 ..