In your sidebar (wherever you want the comments to appear), copy and paste the following code.
<mainpage>
<h2 class="sidebar-title">Recent Comments</h2>
<ul>
<blogger>
<blogitemcommentsenabled>
<blogitemcomments>
<li><$BlogCommentAuthor$> //
<a href="http://www.blogger.com/post-edit.g?blogID=22689915&postID=114046704988137018">">
<$BlogCommentDateTime$></a></li>
</blogitemcomments>
</blogitemcommentsenabled>
</blogger>
</ul>
</mainpage>
A brief look at what this code does.
<mainpage>This means that the following code (until the
</mainpage>) will only appear on the front page of your site. The archive pages (with a separate post on each page) will already be displaying the comments by default, so there isn't much sense in duplicating this.<blogger>This will loop through each post on the page.
<blogitemcommentsenabled>This tag checks to see that comments have been enabled for each post.
<blogitemcomments>Loops through each comment for the post.
NB : This isn't strictly a list of recent comments, but it will certainly give you a good idea. It is, in fact, a list of comments for the posts on that page. There are other techniques for generating a true weblog-wide comment listing, but they each have their own drawbacks and will be covered in a separate post.