It is not immediately obvious how you would get your Twitter updates (which Twitter calls " Twitter badges") to automatically show up on your site or blog pages. But the information is there.
On the next page, you will be shown the choice between either a Flash or a HTML widget. I won't take you through the steps as it is quite easy to figure out from here.
What I do want to note that if you choose the Flash widget, you can change the size of the widget in the code you will be given. (There is also a short note on the site that will point that out).
If you choose the HTML widget, you can change the look, size, colour, etc of it via CSS by using the style identifiers that is in the code you will get. Twitter will not provide you with the styles but if you are familiar with CSS, then this should not be hard.
The Flash widget is .. well, flashier. Of course. It is much prettier and there is no need to fiddle with the CSS styles. They even have a few choices so you can change the look and color of the Flash widget you will get.
However my preference is for the HTML widget. The main reason is because with Flash, Google is not able to read any text. However with the HTML widget, actual text will appear on your site which Google will like. And personally, I do like the CSS which gives you much finer control over the look of things.
You can also read more about how to integrate a Twitter HTML widget into a Drupal site.