How to do the test:

State your Null Hypothesis in the form:
"There is no difference between the populations from which two unrelated samples come" 
Choose a Critical Significance Level (α: alpha):
This is typically α = 0.05. 
Calculate the test statistic:
Use a spreadsheet to calculate your results, or access a helpsheet for SPSS and check here for data entry into SPSS. 
Reject or accept your Null Hypothesis.
Either

Compare the calculated statistic with critical values (Critical values table):
 If r_{S} ≥ r_{S}_{critical} → reject H_{0} → significant result.
 If r_{S} < r_{S}_{critical} → accept H_{0} → nonsignificant result.

Look at the calculated probability (P value):
 If P ≤ α → reject H_{0} → significant result.
 If P > α → accept H_{0} → nonsignificant result.

Compare the calculated statistic with critical values (Critical values table):

Report your results:
Plot your data using the appropriate graphs.
(Spearman Correlation: r_{S} = …, df = …, P = …)