Version 2 is still in development and subjects to changes. It's better to use v1.1 for now.
Version 1.0a is for doing actions on behalf of authenticated user. It needs consumer keys and access tokens.
Version 2 is for doing actions directly from your application. It's suitable to work with public API of twitter, e.g. get a user details.
To work with Oauth v1.0a, there is a nice Node.js package: https://github.com/FeedHive/twitter-api-client/