To change the styling you will need to change the CSS of/within your theme and reference the styles as described. Then you can have your Tweets displayed how you like.
The Tweets are in a widget as with all widgets, and are a simple unordered list.
To make styling easier the <ul> has a class of Tweets – <ul class=”tweets”>
Each Tweet is a list item <li>
Each Time reference is an emphasised link (to your Twitter page) <em><a>
"Your Tweets your way" information above is referenced from here http://www.planet-interactive.co.uk/simple-twitter-tweets/#options