To import your mySQL database from your previous provider, you need to use a MySQL tool such as sqlyog. You can view SQLyog
After you have installed and setup the software, follow these steps:
1) First you will need to open SQLyog. Go to file and connection.
2) You will need to open a connection to your current Mysql database.
3) From the menu go to 'DB', select 'copy database to another host.
4) Enter in the new target (this is your new MySQL database host)
5) Hit copy
This should move the data from one host to another.