The Centre for Learning & Performance Technologies (C4LPT) created a good overview how to use Twitter for social learning. Thanks to Jane Hart for the collected information and the educational scenarios!
Getting Started
Getting started with Twitter
Accessing and using Twitter
The Basics
Building Community on Twitter
Communicating with others on Twitter
Sharing links and resources on Twitter
Keeping up to date on Twitter
Problem solving on Twitter
Serendipitous learning on Twitter
Presentations and Events
Using the Twitter backchannel at an event
Incorporating the Twitter backchannel in a presentation
Live presentation streaming on Twitter
Classes, Training & Learning
Using Twitter in lectures, classes & workshops
Feedback and quizzes
Micro-learning with Twitter
Synchronous learning with live Twitter chats
Other activities
Collaborative writing on Twitter
Games on Twitter
Scavenger hunts on Twitter
Twitter Book Clubs
Managing multiple accounts & networks
Scheduling tweets and managing accounts
Twitter application list
Twitter apps
Reading List
200+ articles about Twitter for Learning
Resource: [C4LPT]
sowebedu 
Using Twitter chats are fundamental to creating an online community of social learning. Check out these chats:
#web20chat
#edchat
#smchat
#realwplearn
Thanks Jeff, for this useful information! 🙂