Once you log in, it will show you a list of your 50 most recent tweets. Click any "Get @s ↑" button to see tweet replies in descending order (newest first). Click any "Get @s ↓" to see tweet replies in ascending order (oldest first). You can also find a specific tweet of yours, and enter the ID number (in red at the end of the twee URL) into the box under the Search tab.
The Conversations page will help you extract a conversation thread with up to ten replies between any amount of people. Unlike the Replies form, a conversation need not be your own for you to extract it here.
Once your replies are display, you can click the Get @ button… and voila! The code is displayed for you. Copy the CSS, HTML or “Full” code and paste it into your blog. If you’re not very familiar with either CSS or HTML, then copy the “Full” code. It will place everything for you on your blog page with nothing additional needed from you!
Chris posted such conversation on his blog : http://chris.pirillo.com/weird-al/. You can check there how it looks like.
Watch the below video where Chris explains more details about Twickie :