On your computer, dump the database
(from command line)
mysqldump -uuser -ppassword database_name > file_name.sql
Then, log into remote server, upload the file_name.sql, and type the following on the command line in the directory where you uploaded the .sql file:
mysql -uuser -ppassword database_name < file_name.sql
This is assuming the database is already created on the remote server, you're just adding the tables. If it's not created, log into mysql and issue the command create database database_name; If it's not your server, you usually don't have permissions to do this, though. Ask your system administrator to create the database for you.
Hope that helps.
---John Holmes...