www.phpmyadmin.net/
if you haven't checked that out, you should. it's php scripts which manage your mysql database.
load it on your local computer, then configure the config file.
you can then backup your table structure + data into a single file.
then, just upload the same scripts to your web host after configuring the config file with the web host info, and you can load up a database with the backup file you made on your local computer.
this is probably the easiest way to accomplish what you are trying to do.
you can backup your mysql database from the command line on your local computer, but you would probably have to use the scripts i mentioned above anyway to get the backup to the web host.
let me know if you have any trouble or questions.