When you perform a linear regression, you're essentially attempting to predict the value of a dependent variable (e.g., as a person's blood sugar level) from a host of other variables (e.g., grams of sugar consumed per day, weight, and height). If the variables are related, you can generate a statistically significant regression model. SPSS  called PASW Statistics after version 17  includes a builtin function for performing regressions.
Things You'll Need
 SPSS (now also known as PASW Statistics 17), any version

Select "Regression > Linear..." from the "Analyze" menu.

Select the dependent variable (the variable whose value you would like to predict; sometimes called "the predicted variable" or "y" in statistics texts) from the dialog box and move it to the text box labeled "Dependent" by clicking the topmost arrow button on the screen.

Select the independent variables (the variables whose values you are using to predict the value of the dependent variable; also sometimes called "the predictor variables" or "x1, x2, x3 ..." in statistics texts) in the box on the left by clicking them. More than one variable can be selected at once by holding the Ctrl key. Move them over to the box labeled "Independent(s)" by clicking the second blue arrow key.

Click OK. SPSS or PASW will display your results in the output window.

Evaluate the results to determine if the correlation is significant. To determine whether your regression was significant, look at the table titled "ANOVA" and view the last column in the "Regression" row. This shows the pvalue (significance value) of your regression as a whole. If it's less than .05, you have a significant regression. Likewise, if you look down at the last column in the "Coefficients" table, you can see the pvalues that your regression model assigned to each of your predictor variables. Those with pvalues that are less that .05 are "significant predictors"  they contributed significant variance with respect to the prediction of the dependent variable.
Tips & Warnings
 In addition to standard regressions, you can perform stepwise, backward, and forward regressions by changing the value of the combo box labeled "Method" (default method is "Enter").
 The "selection variable" box can be used in combination with a rule to restrict your regression to cases that share particular characteristics. For example, if you were correlating the heights and ages of growing teenagers, you could use this method to exclude all individuals with ages greater than 19 from the analysis.
 SPSS identifies numeric variables with little ruler icons. If you see three multicolored balls next to your variable, it means that SPSS has misidentified your variable as a nominal or string variable. If this is the case, you'll need to go into Variable View and change your variable to a numeric variable before continuing.
References
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