Indeed, they are a beast to deal with. The good thing about the mobile design issue is that it's forcing us to reconsider web design practices in general—such as whether drop down menus are even worth having on desktop sites. (IMHO they are terrible things.)
There are some interesting techniques emerging, such as having the menu turn into a single button on a small screen. But that's for simpler menus without drop downs. Other options include restyling the menu entirely on smaller screens so that the top level items are each full width and either lead to their own section where the sub links are then available, or the top level items can be clicked to reveal sub items (as hover basically doesn't work on mobiles).
The first thing to do is work out what you want to do with the menu, and then find a tutorial on how to do it.