You can usually move the actual MySQL database files ( on my iBook they're located in /usr/local/mysql/data/ ) but in general, its not a very good idea. You risk dealing with some wacky permissions issues sometimes, probably more trouble than its worth.
You're best bet is to use this to dump the database:
mysqldump -u username -p your_database > database_dump.sql
And then from the 'mysql' command line utility, use the 'source' command to load it.
mysql> source /path/to/database_dump.sql
