Recently I was working on getting CiviCRM to work with external API access, because I have a multi-site install which needs to be able to communitcate with the contact database across all of the sub-sites without having the plugin turned on (for reasons I'll explain in a moment). Now, API v3 does look like it is a great improvement over v2, however, it has been less-than-documented, and important information is scattered in various locations. I'll try to summarise what I've learned here to illustrate how to get an external API up and running.
The first problem I ran into was the external API script was having trouble finding the civicrm.settings.php file, which is located in /root/sites/default/. The reason this issue occurs is because I have added my civicrm module files to /root/modules/civicrm, instead of /root/sites/all/modules/civicrm/ where it was expecting to be. There's a patch out there that should fix the issue, but you can also get around it by adding a DEFINE('CIVICRM_CONFDIR', '/root/sites/default/'); somewhere in the include path.
The v3 documentation is not very clear about pointing this out, but there are 2 api tokens which you need to get CiviCRM's API to work externally. The first is the 'key' variable, and it is generated when you run the CiviCRM install script when you first install it. It's located in your civicrm.settings.php file as a defined constant. Do a search for 'KEY' and you'll see it. The second is the api_key, which is a bit harder to get at if you don't know where it's coming from. Turns out, it is generated for you each time you start an API session. You log in with a Drupal user who has the appropriate permissions to access the CiviCRM features you're needing to query, using a username and password. This works basically like HTTP basic auth, so watch out if you're doing this locally and not posting to https. (Civicrm's API explorer also generates everything for you as a GET request, so, careful of that as well). However, it'd be too easy if you just logged in with the Drupal user, which leads me to...
The user you are logging in with needs an api_key in the civicrm_contacts table of your CiviCRM database. There does not appear to be a way to generate this via the interface, so you have to go into the database, generate an api key, and drop it in the civicrm_contacts table for the appropriate contact which is tied to the Drupal user you are wanting to use. There may be an extension out there that makes this easier, but I was unable to locate one quickly enough while I was working on my other API issues, so I just manually inserted it.
Now everything seems to be up and running, but it was a bit more of a hassle than I was anticipating. However, I did mention one other problem that I ran into while I was using the api, and the reason I can't use the PHP interface to interact with it directly.
Api/api.php doesn't function if the module is not enabled
I believe this is because the module's autoloader doesn't get called if the module is not enabled on the site you're attempting to interact with it, and could potentially be solved by manually including some files (and this is mentioned on their API docuementation, under a standalone-Joomla! install), which I'll be investigating later. Why don't I just enable the module and be done with it? The issue here is I need to read from the CiviCRM contacts list to ensure some things are there, but I do not want to write to it when a user registers. The CiviCRM module by default implements hook_form_alter and adds the default CiviCRM contact information to the login form, and adds its own form validator and hook_user_presave, which I don't presently want running.
All in all CiviCRM is going to make my life easier, but I really wish the API v3 documentation were fleshed out a bit more, or at least easier to navigate. (Presently you only have the API explorer, which is handy if you know what you're looking for, but not so much if you don't.)