Magento Databases can get pretty big. Here are some commands to help with import/export.
Exporting:
mysqldump -h localhost -u <username> -p <dbname> > <exportname>.sql
Importing:
mysql -h localhost -u <username> -p <dbname> < <importname>.sql
e.g. mysql -h localhost -u karen -p auctionmaid < auctionmaid.sql
If you need to transfer this file off the server via the shell you can do this – see the Putty tools for downloads:
pscp <username>@<remoteip>:<fullpath_to_sql_file>.sql <local_sql_file>.sql
e.g.
pscp root@1.1.1.1:/var/www/vhosts/testsite.com/magdb.sql > magdb.sql