What I meant in my above answer is to post the code here in the forums between backticks- not on your site. Sorry if that was not clear.
Create the widget on Twitter (under your "Settings>Widgets") by clicking on "Create New". You can choose your timeline, your favorites, a list or a search term. Fill out the information requested in the form and then click "Create Widget".
For an example, here's one I created with the code Twitter gives you:
<a class="twitter-timeline" href="https://twitter.com/penelope" data-widget-id="33546993168249XXXX">Tweets by @penelope</a>
Out of all that mess, the only things you want are are the username and the widget id (each widget has its own unique ID#), which goes into the WordPress.com shortcode like this:
[twitter-timeline id=33546993168249XXXX username=penelope]
Of course you use your own unique widget ID# and username once you've created the widget on Twitter. Once you have them, type the twitter-timeline shortcode in a text widget in your site's sidebar.