Use an SSH client, like putty (if your database is on a remote server), to connect to your server and export the databse you want simply with:

mysqldump --user=username --password=1234 --databases your_database --opt --quote-names --allow-keywords --complete-insert | bzip2 -c > your_database.sql.bz2

download the .bz2 file created, unzip it using 7-zip (if you dont have any other uncompress utility), and backup your database in mysql using:

mysql --user=username --password your_database < your_database.sql