Did somebody use phpmyadmin to create this import file?
If so, can you get them to do it again?
If so, can they use the "custom-display all possible options" item in the phpmyadmin export panel? That will allow them to uncheck the "Add CREATE DATABASE / USE statement" and redo the export. That should get rid of your problem with the import.
If you can't get the export file remade, you can use a simple text editor (for example, the notepad program on Windows) to fix up the import SQL file.
If the filename ends in .zip or .gz or some such, you need to uncompress it first.
Then open it up in the text editor. Right near the beginning of the file you'll find lines like these:
--
-- Database: `blah_blah`
--
CREATE DATABASE IF NOT EXISTS `blah_blah` DEFAULT CHARACTER SET latin1 COLLATE latin1_swedish_ci;
USE `blah_blah`;
Delete them and save the file. Then try importing it again.