The simplest integration would just be to launch a web intent to Tweet: https://dev.twitter.com/docs/intents#tweet-intent - but that may run into problems with the WPF control, at least I haven’t heard one way or another whether that would work. You would also need to make sure to clear the cookie store from the web browser control between users, or else they would effectively remain logged into Twitter after Tweeting.
The deeper integration involves using a client library, for example Twitterizer:
http://www.twitterizer.net/documentation/html/008da98c-7349-46d6-b09e-af9f8906eb47.htm
You would need to direct the user to the authorization page, have them complete authorization on Twitter’s UI, and then accept a redirect back to your app. The flow for standard web browsers is documented here: https://dev.twitter.com/docs/auth/browser-sign-flow but it should be pretty similar with the web browser control. Once again, you’ll need to make sure to clear the cookie store between users, or else they’ll see the logged in accept page from the previous user.
