How do you know this module is working

There is no admin interface for this module. Just like other performance modules, this one works with overriding core caching to allow high speed and high performance cache access.

For APC:
You can use the apc.php file that ships with the linux version to view stats in the browser

"Would increase in cached variables under User cache section of APC is an indication?"

- Yes, that's an indication APC is working. The "System Cache" entries indicate cached php opcode files. The "User Cache" entries contain custom drupal cache entries.

For memcached, there are a number of tools for testing it's working, e.g:

http://code.google.com/p/memcached-manager/wiki/Screenshots ( cross platform Python ) or
http://allegiance.chi-town.com/MemCacheDManager.aspx ( Windows )

DT

For file engine, use FTP to observe that there are files created in the configured caching directory.

And for all: Go to your database with PhpMyAdmin, and truncate the cache tables there. This is useful anyway (makes your database backups smaller, and removes the risk of using stale data if you ever revert back to default Drupal caching later), and it doesn't really hurt - the data will be rebuilt ASAP, if the tables are in use. And that's also the point here - if your site works, and the cache tables in database stay empty, then data are stored elsewhere for sure.

This module can't have a proper UI, because it's controlled from settings.php (not from database-stored settings). That's unavoidable here.

I don't understand why the picture on the cacherouter page depicts an admin interface.

Can I use this module with the performance module?

http://drupal.org/node/330237

For those who are using memcache, you can also use memcache.php.

Just add the file where ever your code is, change the password and view it on your browser.

[edit]

This is a duplication of: http://drupal.org/node/448274