How do I check APC cache is running? The best way is to browse apc.php
When I install PHP one of the first things I do is copy the apc.php file into my web rootcopy the apc.php file into my web root.
cp /usr/share/doc/php-apc/apc.php /var/www/public/apc.php
You can then go to domain.com/apc.php and view what is being cached, clear the cache, check on memory usage etc
You may need to edit apc.php and set a password to access some features but that should be straight forward.
What is the correct command to install APC cache
'apt-get install package' is correct, your package will depend on what version of debian you're using, for example squeeze uses php-apcphp-apc http://packages.debian.org/squeeze/php/php-apc