Shell or Telnet or SSH is something that any system administrator can not live without. It's a necessary lifeline when it comes to VPS and Dedicated Servers. If your host doesn't offer it, switch to Hands-on Web Hosting as it will make your life much easier when doing routine tasks such as backing up a database, copying a database or importing a database.
Dealing with databases all day long in the eComemrce world we are constantly importing SQL files or making backups for users for whatever reason, shell is the easiest (and fastest) way to do this.
To export a database we use the command "mysqldump":
mysqldump -u username -ppassword database_name > file.sql
If you are ROOT you can do something simple like:
mysqldump database_name > file.sql
To import a database we use just the straight command "mysql" command:
mysql -u username -ppassword database_name < file.sql
Or if you are logged in as root you can do just:
mysql database_name < file.sql
The database MUST exist if you run this process for the import.