The best answer is phpMyAdmin.

There are numerous ways to upload a MySQL database, we would strongly recommend trying methods 2 and 3 

Method 1 – phpMyAdmin 

You may use phpMyAdmin to load your database by using the Import link to upload a .sql file or by pasting the SQL script into a query window and executing it. For the latter method - 

1. Login to phpMyAdmin with a MySQL user that has been given DBA rights to the MySQL database you wish to load. 
2. Then click on the SQL tab. 
3. Paste the SQL script content into the text area, and click Go. 

If the SQL script contains a lot of data, you might still get away with this by pasting it bit by bit. If the data is simply too large, see the other sections. 

Method 2 - Web Hosting Control Panel control panel restore 

In the Web Hosting Control Panel control panel go to the MySQL Databases page. 
On this page is the text "To restore a database which you've previously backed up, click here." 
If you follow the link, you can upload a larger SQL file than would be possible in phpMyAdmin. 

If the SQL file is very large, please consider one of the other methods below 

Method 3 - MySQL Administrator 

MySQL offer free software to manage, backup and restore MySQL databases. 
The software can restore very large files, and also comes packaged with MySQL Query Browser, which can be used a faster alternative to phpMyAdmin 
You can download the software at http://dev.mysql.com/downloads/gui-tools/5.0.html 

Method 4 - MySQL command line client 

This requires you to have SSH Access, which may or may not be available on your particular package. 
Due to the limitations imposed by PHP, phpMyAdmin is unable to load a large MySQL dump data. 

You can upload the MySQL dump file created by mysqldump --opt -Q dbname to your home directory, and then execute the MySQL client to load it. 

To load your sql dump using MySQL, you can use the following command: 

mysql -h mysqlhost -u mysqlusername -p databasename < dumpfile.sql 

or 

cat dumpfile | mysql -h mysqlhost -u mysqlusername -p databasename 

Where: 

mysqlhost - The name of the server where your MySQL database is located. You can find this out from the Control Panel in the MySQL Database area.
mysqlusername - Your MySQL User name as created through the Control Panel. 
databasename - This is the name of your database 
dumpfile.sql - The file created by mysqldump