The main display module is pretty simple to move around if you are familiar with WP and short codes.
If you’d like to move the post-story module, you can override the default placement in your theme files.
In Wordpress, look on the left control bar for Appearance. Then choose Editor. You’ll then want to make changes to the Single Post file. It’s usually listed at the bottom and is named single.php
Before you make changes to this file, copy and paste the existing file and save it on your computer as a text file. That way if something goes wonky, it’s super-simple to revert.
Find the spot you’d like the display to show up at. Paste in the following: <?php echo do_shortcode('[contextly_main_module]'); ?>
You can then save the file and go look at a live page to see if it’s where you want it. If it's not in the right spot, just move that line of code around until you find the sweet spot.