There might be an easier way than the one I'm about to suggest but it probably depends on your permissions within phpmyadmin.
On the main page once you have logged into phpmyadmin, click on 'Export.'
Then highlight the database whose structure you want to copy. Choose 'SQL' underneath that. Then make sure that ONLY 'Structure' checkbox is checked. If anything else is, then uncheck it...especially 'Data.' Click 'Go.'
The output should be valid SQL for you to copy and paste into the SQL textbox on the SQL tab. Before doing so, however, in the output that was generated make sure you change the name of the database you copied to the name you want the new one to have. Example would be if your existing database was called old_db, then:
CREATE DATABASE `old_db`;
USE old_db;
Should now be:
CREATE DATABASE `new_db`;
USE new_db;
Sorry this got so long...