On the SitePoint blogs today there's a new tutorial posted, the first part of a series, from Raj Deut about making the move away from the basic authorization for connecting to the Twitter API and towards their new OAuth method for Twitter Apps.
As of August 31, Twitter's HTTP Basic Authenticated API service has been disabled entirely. Now, any interface with the API will be required to use a token-based authentication method known an OAuth. [...] At first glance, the task of implementing OAuth can appear daunting, and OAuth's token exchange system can be confusing if you're unfamiliar with it. Fortunately, there are some rather clever individuals who've done the groundwork for us.
They show you how to register your application with Twitter and use the TwitterOAuth library to make a sample connection to their servers. They also show how to generate the tokens for the URL and the ones for accessing the site as a user. With tokens in hand, the script can then connect to the system and make a sample tweet (complete code included).