How can I export the privileges from MySQL and then import to a new server?

Do not mess with the mysql db. There is a lot more going on there than just the users table. Your best bet is the "SHOW GRANTS FOR" command. I have a lot of CLI maintenance aliases and functions in my .bashrc (actually my .bash_aliases that I source in my .bashrc). This function:

mygrants()
{
  mysql -B -N $@ -e "SELECT DISTINCT CONCAT(
    'SHOW GRANTS FOR \'', user, '\'@\'', host, '\';'
    ) AS query FROM mysql.user" | \
  mysql $@ | \
  sed 's/\(GRANT .*\)/\1;/;s/^\(Grants for .*\)/## \1 ##/;/##/{x;p;x;}'
}

The first mysql command uses SQL to generate valid SQL which is piped to the second mysql command. The output is then piped through sed to add pretty comments.

The $@ in the command will allow you to call it as: mygrants --host=prod-db1 --user=admin --password=secret

You can use your full unix tool kit on this like so:

mygrants --host=prod-db1 --user=admin --password=secret | grep rails_admin | mysql --host=staging-db1 --user=admin --password=secret

That is THE right way to move users. Your MySQL ACL is modified with pure SQL.

There are two methods for extracting SQL Grants from a MySQL Instance

METHOD #1

You can use pt-show-grants from Percona Toolkit

MYSQL_CONN="-uroot -ppassword"
pt-show-grants ${MYSQL_CONN} > MySQLUserGrants.sql

METHOD #2

You can emulate pt-show-grants with the following

MYSQL_CONN="-uroot -ppassword"
mysql ${MYSQL_CONN} --skip-column-names -A -e"SELECT CONCAT('SHOW GRANTS FOR ''',user,'''@''',host,''';') FROM mysql.user WHERE user<>''" | mysql ${MYSQL_CONN} --skip-column-names -A | sed 's/$/;/g' > MySQLUserGrants.sql

Either method will produce a pure SQL dump of the MySQL grants. All there is left to do is to execute the script on a new server:

mysql -uroot -p -A < MySQLUserGrants.sql

Give it a Try !!!