The Intention:
APC, or Alternative PHP Cache can benefit performance of a Drupal site by caching core php functions.

The Configuration:
WAMP 2.4 32 bit
Windows Server 2012
PHP 5.4.16

The Problem:
Since we're on Windows, we need a .dll to put in our php ext folder. I went, naturally, to the following site: http://pecl.php.net/package/APC. This site gives you three options at the time of writing this post: 3.1.11, 3.1.12, 3.1.13. None of these work.

I kept getting tons of unhelpful errors. Loads of them. Some included things like "Unknown: apc_cache_find", and an example of a similar error I found was on http://forums.devnetwork.net/viewtopic.php?f=1&t=130217

The Solution:

http://downloads.php.net/pierre/

This guy had 3.1.10. It worked.

Installation Instructions:

Drop that php_apc.dll in the C:\wamp\bin\php\php5.4.16\ext folder.

In your WAMP Manager icon on the bottom right, go to the PHP folder, then to the php.ini file.
Halfway down that file, you're going to see about 25 line items that look similar to the below, and you're going to want to add this to the list.

extension=php_apc.dll

Don't save and close yet! At the bottom of the php.ini file, add the following:

[apc]
apc.shm_size = 128M
apc.rfc1867 = 1

This will turn off other random error messages.

Save and close.

In WAMP Manager, restart the apache service.