you usually have to use mysqldump from the command line (via SSH using puTTY or other terminal program) and if you don't have command line access it gets dodgy because you have to go through all kinds of other trouble.
if your database is small, phpmyadmin can be really easy to use.
Roger's right about the workbench app, but it takes some getting used to (well worth it in the long run but perhaps risky if you are facing a deadline).