How do I create side by side images on a post page?

To create side by side images, also called a diptych, first click the Add Media button. You can either upload two images or select two that you have already uploaded.

Then, click the Create Gallery link and click the Create a new gallery button to continue.

In the gallery settings, select link to none, then change the columns to 2, and select the Full Size. Then, insert gallery! Your theme will take care of the rest. See it in action in the video below: