If you write your own code, you’ll have to write the OAuth part, which is documented at https://dev.twitter.com/docs/auth. You could use HttpClient to make the rest calls to the statuses/update endpoint, documented at https://dev.twitter.com/docs/api/1.1/post/statuses/update.
Alternatively, you can use a 3rd party library, listed at https://dev.twitter.com/docs/twitter-libraries. BTW, I wrote LINQ to Twitter - https://linqtotwitter.codeplex.com/, which contains technical documentation, FAQ, examples, and demo code. The downloadable source code has examples for both Web Forms and MVC.
