By default, a user can quickly close a displayed PX Dialog Engagement by using the small “X” close icon in the top right corner (or by clicking the “Esc” keyboard key). Sometimes the small “X” can be hard to see, so the Engagement author/editor can also change the small “X” close icon to use a different image and even move the location too, so see this previous PX Community Post for more details.
A simpler option that does not require CSS editing is to add any custom button in the Engagement, which will accomplish the same thing as the default “X” close icon.
If you add a custom button, the default user experience when clicked is that the current page in your application will refresh. If you do not want the page refresh to happen, then you can edit the HTML source code of the button to specify the "onclick" property just like the following:
<a href="#" onclick="return false;">Close Me, Do Not Refresh My Page</a>
Happy PX-ing!