Having got used to the Debian package naming conventions, I thought I’d install APC with this:

# apt-get install php5-apc

Turns out, it’s actually this:

# apt-cache search apc  
==> php-apc - APC (Alternative PHP Cache) module for PHP 5

Install, and reload:

# apt-get install php-apc
# /etc/init.d/php-fpm reload