How would I create a website drop down menu like this websites?

The site is using a free program called Java to create the drop down menu. If you do a search for "java drop down menus" you will find dozens of different sites that offer free menu systems in Java that you can download and then customize to work with your site.

While it not be exactly how that particular website does it, the easiest way to create a drop down list is to use html and css.

Basically the menu is implemented in html as a couple of embedded bullet lists, and css is used to pretty them up such that they display like menus. Using css code you set display to none for the menu options when your menu is not being moused over; then in the css for the pseudo class :hover you set display to block so that when oyu mouse over it the menu displays. Thats a pretty terrible explanation but this is a good tutorial which helped me learn how to do it when I wanted to do it in an assignment last year:

http://www.ssi-developer.net/css/menu-rollover-eff...

Otherwise if you don't want to do it yourself; or want to read through completed code to try and understand it (which helped me figure it out) then http://www.cssmenumaker.com/ generates them according to settings you pick.

Drop down menus do not require Javascript; however with websites not supporting the feature fully, it acts like a hack to work around that.

http://www.dynamicdrive.com/dynamicindex1/

While I'm not a web design expert, from what I do know, those are called "Spry Accordions."

Although, that may only work with Adobe software.

http://en.wikipedia.org/wiki/Spry_framework