After having a look at Apple TWRequest class (and example), I was surprised it has no possibilities for presenting a user with a login screen. The only way is to check if a user has entered its credentials with [TWTweetComposeViewController canSendTweet] and if no then give a message like
"Hey, you have manually to go to settings->twitter and enter the credentials. Then you should find and open our app manually and continue on"
I'm wondering does anybody use such crap functionality :) For example, Facebook iOS SDK 3 has implemented Single Sign On (SSO) that opens Safari with Facebook login screen and returns to your app after login... I guess I will need to fallback to old styled twitter integration with a lot of 3rd party stuff.
ps. I would give a try to ShareKit but I need to integrate my app with google+ which is not currently supported in ShareKit.