Help me understand a 3d graph I've just seen this graph and while it's isn't the first 3d graph I've seen, as
a math "noob" I never thought how these graphs are plotted. I can draw 2d graphs on paper by marking the input and output values of a function. It's also easy for me to visualize what the graph I'm seeing says about the function but what about graphs for functions with 2 variables? How do I approach drawing and understanding the visualization? 

Set your function equal to a given constant, this give you a function you are used to, and varying the height (ie what you set your function equal to) gives you the graph (2d) of the surface intersected with planes parallel to the xy-plane.  Its essentially the same as a contour map of a mountain.
