Caching

This has to be done for each site. This is after installing Memcache on your server.

Memcache module

Then, in settings.php, add:

The error messages Varnish provides are very informative.

tail -f /var/log/varnish/current

On admin/config/development/performance

Minimum cache lifetime
Cached pages will not be re-created until at least this much time has elapsed.
Expiration of cached pages
The maximum time an external cache can use an old version of a page.

What exactly does each mean?

This is quite a major point of confusion for Drupal 6:

http://drupal.org/node/142242#comment-230669