1) Select the database you wish to copy (by clicking on the database from the phpMyAdmin home screen).
2) Once inside the database, select the Operations tab.
3) Scroll down to the section where it says "Copy database to:"
4) Type in the name of the new database.
5) Select "structure and data" to copy everything.  Alternately, you can select "Structure only" if you want the columns but not the data.
6) Check the box "CREATE DATABASE before copying" to create a new database.
7) Check the box "Add AUTO_INCREMENT value."
8) Click on the Go button to proceed.