LibGuides have a variety of widgets that you can use to make drop-down menus. You can access the widget page by logging in to LibGuides and selecting the "Tools" option from the top menu and then "Widgets."
The first tab will let you make a widget listing all your guides. As you select options, the preview of your widget will be shown on the right-hand side of the screen. Once you are happy with your widget, copy the embed code and paste it into a new widget.
Here's a simple drop-down menu showing all of the Aestiva LibGuides.
The next tab will create a drop-down menu listing all of your databases. Many of the options are the same.
You can also create drop-down menus for users, subjects, and groups.