In a new tutorial from NETTUTS.com today they look at connecting Twitter and your CodeIgniter-based application via a curl interface (and caching the last tweet).
They help you configure your framework to autoload the database, create the table and built the model to fetch the latest tweets. Another function (update()) is created to post a new message out to the Twitter API. This involves a simple input form with a bit of validation wrapped around it.
Add in a few views to display the results to the user and some CSS to style it and you're all done. The post has the full code and screenshots included.