If you are interested in learning how to build responsive websites, you should consider enrolling in our free online course, Responsive Web Design.
If you are at all on the fence, below is a brief excerpt from the course. In it our instructor, Jeremy Osborn, describes the challenges associated with "responsive navigation." Some of these challenges—what to relegate to secondary navigation versus primary; whether to rely on single-level navigation or multi-level—are part of designing site navigation in general.
Other challenges, however, are specific to responsive site design. For example, you could simply allow your navigation elements to wrap as the screen gets smaller, although this quickly becomes problematic if you are dealing with a lot of elements.
On the other hand, you could use media queries to "stack" the navigation elements. This solution is fairly easy to execute and can be good for small touch screens. At the same time, if you are dealing with a lot of elements, your stacked navigation can quickly eat up screen space, which is far from optimal.
Here's how Jeremy describes the issues and alternatives when it comes to responsive navigation design: