At long last we come to the method for graphing the function z = f(x,y) that is easiest to understand, but most difficult to accomplish (since we don't have 3D computer screens or paper.) How did you learn to graph the function y = f(x) first? By plotting points. That method works here as well, it just gets difficult to plot all of the ordered triples (x,y,f(x,y)) and make sense out of them. It's easier if you know something about the function. Maybe it's just a translation or scaling of a familiar function. Maybe not.
Sometimes, you just have to try plotting points. If that's necessary, here's a quick graphical tour through the technique. Start with a table of points that lie on the function z = e-(x2 + y2).
Now, turn the table so that it's positioned as the xy-plane in 3D perspective.
Now, each entry in the table is a z value. This is the distance that each square of the table should be raised above the xy-plane in order to form the surface.
When you're done, you'll have a sort of block form picture of the surface.
This can be smoothed out, but you get the idea. It's much easier if the function is familiar and is simply a translation, reflection, or scaling of the original function. Sometimes, you may need to make a contour plot or sectioning or both in order to help visualize what the surface is. Use every tool at your disposal.