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I don't see how this is done. I can find what seems to be a box but there are no parameter for entering list items.
A drop down list like for a web page? That requires HTML code. It's not a "design" thing.
You're going to have provide a lot more information. What version of InDesign? What are you planning on exporting to? How will it be viewed?
For a PDF form, you can add a Combo Box (drop down). If that is what you need, take a look at screen capture.
To make an element a Combo Box, contextual select frame, Interactive > Convert to Combo Box.
To add the choices of the Combo Box, from Buttons and Forms panel, add your content to the List Item Field, and then select the + button to add to list.
Perhaps this is an older version because I'm not seeing what you are . I'm using 2015.3, build 184.108.40.206x64
I can find what seems to be a box but there are no parameter for entering list items.
You can do this as form field.
Export as an Interactive PDF. It won't work inside of InDesign.
Is this what you are asking?
If you want to create a functional menu that works in epub, Publish Online, and in5 (HTML5), without coding...there's a technique described in this guide:
in5 also comes with a Menu Builder wizard that can help with this. Shown in this video: