If you are new to Twitter then have a look at this tube map of tweeting teachers by @Pekabelo, it will give you a good starting position to follow teachers already engaged in peer to peer learning via twitter:
How teachers are using Twitter via @dailygenius:
Below is an infograhpic made by @TeamTait detailing when Twitter chats are on this year – if you need any help or advice on accessing these please come and see me. Just click on the infographic to enlarge.
25 things teachers have found and used on Twitter