Right on... First thing is you should read up on the loop. Just to gain a bit of understanding. Then read a bit about Template Tags. Once you read these documents, it should be really easy for you to switch the code...
Basically, There are tamplate tags which generate the following code in your blog:
<div class="entry-meta">
<span class="meta-start">Published</span> <div class="entry-author"><span class="meta-prep">by</span> <address class="vcard author"><a href="http://www.inkdryerdesign.com/blog/?author=2" class="url fn" title="View all posts by Chris">Chris</a></address></div> <div class="entry-date"><span class="meta-prep">on</span> <abbr class="published" title="2009-01-08T02:51:15-0700">January 8, 2009</abbr></div> <div class="entry-categories"><span class="meta-prep">in</span> <a href="http://www.inkdryerdesign.com/blog/?cat=1" title="View all posts in Uncategorized">Uncategorized</a></div><span class="meta-end">.</span>
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</div> <!-- .entry-meta -->
The short answer is to move everything between <div class="entry-meta"> and <!-- .entry-meta --> below the "the_content()" template tag. Will will most likely have to do this in more than one file.