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? 

It's the same idea as a two-dimensional graph.  Instead of one variable for input, you have two, so instead of a line for inputs you need a plane for inputs.  Then, if it's a real-valued function, $f(x,y)$ is a real value, so you still only need one line for output.
Then, over the input plane, you place the points $(x, y, f(x,y))$.
