How do I make a new style show up in the styles list?

Make sure that the "Add to the Styles gallery" check box in the Modify Style dialog is ticked:

The default display option for the Styles pane is "Recommended." If you click on Options... in the bottom right corner of the pane, you can change this to "In use," "In current document," or "All styles." The last will certainly display a new style (and either of the others may), and it will be easier to find if you change the sort order to "Alphabetical." You can also use the Manage Styles dialog (accessed from the third button on the left at the bottom of the pane) to assign a higher priority to the style.

That said, a list style will never be displayed in the Styles pane; only the individual styles linked to the list levels are displayed. You start the list by applying one of those styles.

Click the little arrow in the lower right corner of the Styles group on the Home tab of the ribbon to display the Styles task pane.

Click Options... near the bottom of the Styles task pane:

In the Style Pane Options dialog, select 'All styles' from the 'Select styles to show' dropdown.

You may also want to select 'Alphabetical' from the 'Select how list is sorted' dropdown.

Then click OK.

You should now be able to find your style in the list of all styles. Right-click it and select Modify...

Did you click Options and select All styles? If so, Body Text should be listed:

After you have assigned a priority level to your custom style in the Manage Styles dialog box, you have to make sure that the Style Pane Options dialog box displays the "Recommended" styles (or "All styles" of course).

Also, remember that the style resides in the document where you created it. You have to add it to your template if you want to see it in all new documents based on that template.

To clarify, the Styles pane only displays character and paragraph styles (your screen shot shows as an example the "Body Text" paragraph style). List styles (and table styles) never show up in that pane.