There is a great guide on that by Linda Rhodes Shanock and collegues, I have added it in the attachment.
This is an analysis in spss, you enter the numbers you get from the polynomial regression in spss in an excel sheet, which produces the Response Surface graph.
Article Erratum to: Polynomial Regression with Response Surface Anal...
SPSS does not have a defined "Response Surface" analysis capability. If you put your data with the levels you tested into SPSS, you can recreate the coefficients for you model. However, SPSS will think that your factors are highly correlated with each other. So, using SPSS with actual levels will give you a different/false final model. To get around this, you need to go back and code your variables the way Design Expert, Minitab, JMP or Umetrics would do.
Suppose that you tested temperatures of 50, 100, 150, 200 and 250. To code these variables like how the software above would do it, you need to recode the levels as, -2, -1, 0, 1, 2. Using SPSS on this data will give you the correct model but the coefficients will be wrong.
Most of the time, after you create your final model, you want to "optimize" it somehow. SPSS does not have this option. I would save myself some time and headache and just use Design Expert or JMP.
The open-source software package R has a response surface analysis package called 'rsm.' I would recommend the attached publication as a starting point, which thoroughly explains response surface analysis. R has a somewhat steep initial learning curve, but because it's open-source it's free and your analysis will be easily reproducible.
Note that if you wish to compare results between R and JMP that R uses Type I Sums of Squares as its default, while JMP uses Type III. The 'car' package contains a function which permits easy calculation of Type III Sums of Squares (in case you wind up comparing results between JMP and R and get confused because the F-statistics and p-values differ between the two).