Just wondering if anyone can give a brief overview on how to take a hand drawn image and turn it into a decent looking vector image? I have no idea where to start.

Well, I suppose each artist has their own preference for this process, and their own style. I guess usually the image would be scanned onto the hard drive. Then it could be imported to Inkscape, and then traced "by hand" with the Pen/Bezier, Pencil or Calligraphy tool.

If you're not exactly an artist, or don't want to do a lot of Inkscape work "by hand", you could try using Path menu > Trace Bitmap. You'll probably still need to do some touch-up work, but not nearly as much as doing it all by hand. (http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Trace.html)

A lot of artists use a graphics pen and tablet (such as Wacom) (not like iPad tablet) which allows them to draw the image directly into Inkscape. For them, it seems to be preferable to using the mouse.

Also, I found that the Help menu > Tutorials were especially helpful when I was first starting to learn Inkscape. Once you know a little more about the basic tools, you'll be able to start developing your own style

I'm the co-creator of a couple of webcomics, one drawn entirely in Inkscape, and the other drawn by hand then traced and coloured in Inkscape. The processes we use for both types of strips are described in some detail in this thread.

If you want some more specific information it might be worth telling us what type of drawings you'd like to create. Creating a freehand comic look will probably entail different tools and methods to converting a crisp logo design from a hand drawn sketch to a vector, so a little more detail might get you some more directly relevant suggestions.