Need help customizing individual comments

To make the change you want you will firstly have to turn off the threaded comments. This you do in Settings, Discussion. After this you need to style the comments in your stylesheet. Most of these changes will have to be made to the commentlist element.

I understand how to stylize the CSS elements. However, I’m trying to rearrange the placement of comment tags such as author, date, comment text, etc. Where can I edit these?

This depends entirely on your theme.