Depending on your preferences, it might be worth looking into Twitter4J - Twitter4J is a Java
library that provides a standard API around the Twitter user web services and provides all the objects you need to tweet, re-tweet, view users timelines, profiles etc.
Twitter authentication is done using OAuth, so you need to register for your application details on the Twitter site.
There is an example (plus source code) of very basic twitter functionality here: http://automateddeveloper.blogspot.com/2011/05/android-twitter-reader.html
although it doesn't include the OAuth or updating stuff, it should give you an idea of how the Twitter4J API looks and how easy it sits with Android.
If you prefer to work with WebServices/JSON then you can just use the direct Twitter Web Services.
When developing the app, you will need to take care to optimize the caching etc, as Twitter limits the number of requests that can be made per hour, and if you dont manage the requests properly you can quite quickly hit the limit.