To tell how many files MySQL has open, you need to login as root and run one of the following commands:

# lsof | grep mysql

# lsof | grep mysqld

# lsof -c mysqld

# ls -l /proc/<PID>/fd  /* where <PID> is the process ID of the program you are interested in */

# lsof | grep "/var/lib/mysql"

You can tell how many files your OS has opened with this:

# cat /proc/sys/fs/file-max

On a MySQL client, you can run the following:

SHOW OPEN TABLES

To close the open files run:
FLUSH TABLES