You can obtain a copy of MySQL Workbench here: http://dev.mysql.com/downloads/workbench/5.2.html
Once you have installed MySQL Workbench launch it and under the "Server Administration" click on "New Server Instance". This will pull up a new Instance wizard.
Under the "Specify the Host Machine the Database Server is running on" click on "Remote Host" and for the address put an IP of the server that your database is on.
Under the "Set the Database Connection values" screen you can leave "Connection Name" the same as the server IP or change it to something more meaningful like "My wordpress database server". Leave "Connection Method" as "Standard (TCP/IP)". Under the "Parameters" tab make sure that hostname matches the IP from the previous step. Leave port as "3306" and enter your database username. Click on "Store in Vault" and enter the password for the above user. Leave "Default Schema" empty".
Testing the connection should give you three check marks and show "Database connection tested successfully." Click on "Next".
On "Set remote configuration parameters" UNCHECK "Enable SSH login based administration" and click on "Next".
Under "Create the Instance Profile" you can use something like "My backup" and click "Finish".
After the steps above your "Workbench Central" should now have new connection listed under the "Server Administration" on the right. Click on "Manage Import / Export" link and then from the pop-up window click the instance you created earlier.
Under the "Export to Disk" tab place a check-mark next to your database name. Under "Options" to the right check "Export to Self-Contained File" and click on "Start Export".