You may show/hide columns, reorder fields, and save layout preferences.
Instructions
Once you have your desired layout, click Query Layout in the bottom-left of the screen

Click New

Once you select New, you will then be prompted to name the new layout. There is an optional note field as well:

Name: Name the layout
Note: Type any notes for this layout
Private or Share With: Mark this layout Private, or select a list of users to share the layout with
Default: Make this layout the default layout
Click Save

Note:
Any saved layouts will be visible at the top of the query layout screen.