How do I create an Android Spinner as a popup?

You can use an alert dialog

    AlertDialog.Builder b = new Builder(this);
    b.setTitle("Example");
    String[] types = {"By Zip", "By Category"};
    b.setItems(types, new OnClickListener() {
        
        @Override
        public void onClick(DialogInterface dialog, int which) {
            
            dialog.dismiss();
            switch(which){
            case 0:
                onZipRequested();
                break;
            case 1:
                onCategoryRequested();
                break;
            }
        }

    });

    b.show();

This will close the dialog when one of them is pressed like you are wanting.