Michelangelo van Dam's Blog: Single User Zend_Service_Twitter
Michelangelo van Dam has a new post to his blog today with an example of using the Zend_Service_Twitter component of the Zend Framework to set up a simple Twitter client to connect and grab the latest tweets from an account.
Although the Zend Framework manual extensively describes how to set up a true Twitter application with the new OAuth implementation of Twitter using Zend_Service_Twitter and Zend_Oauth (since ZF-1.10.0), this is not what you're looking for. You need a simple approach, using the single user OAuth implementation of Twitter.
He shows (complete with screenshots) how to register for access to the Twitter API and how, once you've grabbed your access tokens, to pull the latest tweets from the selected account - complete with a code sample to show you how. It's a Zend Framework-specific example, but the components can be used outside the framework for the same effect.