The Twitter field works for two kinds of Twitter input: a handle, or a hashtag.
To add a Twitter follow button to a profile on your site, simply put the Twitter "handle" in the proper box under the Contact info tab. A Twitter handle starts with the @ symbol, as you see below. Advanced mode may need to be turned on to see the Contact info tab (bottom right of your screen - will turn blue when engaged).
Once you save the post, it will look something like this:
Note that you can add a Twitter hashtag, instead of the user handle, if you'd like. This adds "Tweet this" functionality for the subject you've included in the field. Hashtags always start with the pound sign, for example #digdep.
This is what it looks like after you save your post, and a "Tweet this" button is added:
Once the user clicks the Tweet button, they'll see the following screen (or a prompt to log in first)