mysql db_name < script.sql

If you are using phpMyAdmin, you can simply create a database and then go to the import tab and upload there, or you can SSH to your server and run 'mysql -u username -ppassword database_name < FILE.sql'.
Make sure -ppassword has your password after it with no spaces.

Let's say you want to import a mysql dump into a new database with a new user.
Where your mysqldump is source.sql

# Enter into MySQL using "root" user identified by password
mysql -u root -p

#Create the database
mysql> CREATE DATABASE NEWDB;

#Create the user
mysql> CREATE USER 'newuser'@'localhsot' IDENTIFIED BY 'newpass';

#Grant ALL privileges onthe new database to the new User
mysql> GRANT ALL PRIVILEGES ON NEWDB.* TO 'newuser'@'localhost' IDENTIFIED BY 'newpass';

#Switch to the New Database
mysql> USE NEWDB;

#Insert data from source.sql
mysql> SOURCE source.sql

Thanks for all of those ways to import into mysql. I got that working. Yay.