The mysql data should download to your browser's default download destination.
If you get any Table already exists errors while importing data, re-save the sql with the *Add drop table* option checked, or simply delete the conflicting tables and run the import again.
cd to whatever directory you wish to store the data, and enter:
mysqldump --default-character-set=latin1 -C -u USERNAME -p --opt --lock-tables=false --skip-add-locks --skip-extended-insert DATABASE > DATABASE.sql
Make sure you replace the values in CAPS with the correct info for your account (you can also change the character set if you wish).
To tgz compress the file DATABASE.sql for easier transportation:
tar czvf DATABASE.tgz DATABASE.sql
cd to wherever the sql data is stored, and enter:
mysql -uUSER -pPASSWORD DATABASE < DATABASE.sql
Again, make sure to replace the values in CAPS.