Well there are four possible approaches that come to mind (although I am sure that there are many more) but basically you could either plot the data as a perspective plot, a contour plot, a heat map or if you prefer a 3-D scatter plot (which is more or less a perspective plot when you have values of $z$ for all $(x,y)$ pairs.  Here are some examples of each (from a well known 3-D data set in `R`):


![enter image description here][1]
![enter image description here][2]
![enter image description here][3]
![enter image description here][4]

So depending on your preference will dictate which way you like to visualize 3-D data sets.


Here is the `R` code used to generate these four mentioned plots.

   

     library(scatterplot3d)
        
        #Data for illistarition
        x = seq(-10, 10, length= 100)
        y = x
        f = function(x, y) { r = sqrt(x^2+y^2); 10 * sin(r)/r }
        z = outer(x, y, f)
        z[is.na(z)] = 1
        
        #Method 1
        #Perspective Plot
        persp(x,y,z,col="lightblue",main="Perspective Plot")
        
        #Method 2
        #Contour Plot
        contour(x,y,z,main="Contour Plot")
        
        #Method 3
        #Heatmap
        image(x,y,z,main="Heat Map")
        
        #Method 4
        #3-D Scatter Plot
        X = expand.grid(x,y)
        x = X[,1]
        y = X[,2]
        z = c(z)
        scatterplot3d(x,y,z,color="lightblue",pch=21,main="3-D Scatter Plot")


  [1]: https://i.sstatic.net/sfGra.png
  [2]: https://i.sstatic.net/x1w95.png
  [3]: https://i.sstatic.net/wMq9m.png
  [4]: https://i.sstatic.net/NMxHY.png