Click Analyze > Correlate > Partial... on the menu system, as shown below:

Published with written permission from SPSS Statistics, IBM Corporation.

You will be presented with the following Partial Correlations screen:

Published with written permission from SPSS Statistics, IBM Corporation.

Transfer the variables weight and VO2max into the Variables: box, and age into the Controlling for: box, by dragging-and-dropping or by clicking the relevant  buttons. You will end up with a screen similar to the one below:

Published with written permission from SPSS Statistics, IBM Corporation.

Click the  button. You will be presented with the following Partial Correlations: Options screen:

Published with written permission from SPSS Statistics, IBM Corporation.

Tick the Means and standard deviations and Zero-order correlations checkbox in the –Statistics– area, as shown below:

Published with written permission from SPSS Statistics, IBM Corporation.

Click the  button.

Click the  button. This will generate the results.