Head over to analytics.twitter.com and sign in using your twitter username and password.
It’s basically developed for advertisers, so it’ll ask you some information. If you’re not an advertiser, then look up to navigation area and click on the analytics link.
With Twitter analytics you can look at the best performing tweets, number of retweets, no of people favored your tweets, responses to your tweets etc.. you can even download this data in CSV format.
API – Application Programming Interface
Twitter is reportedly going to stop with old API, and is going to introduce new set of API’s. Hope these analytics API’s will also be publicly released, so that developers could build wonderful applications.