Database export via phpMyAdmin

The size of the database dump can be many times smaller than the size of the hosted database.
  1. Signin in phpMyAdmin.
  2. Select a database from the list on the left:
  3. Open the tab "Export", make sure the radio button is set next to the method "Quick" and in the field "Format" selected "SQL", and press "Forward":

As a result, a file in SQL format will be downloaded with the current contents of the database. The resulting file can be used for subsequent import.