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Use a post map to label a vector map with the magnitude data. To do this, follow these steps:

1. Calculate the gradient (magnitude) by going to Grid | Calculus. Select your grid and click Open.

2. Choose the Differential & Integral Operator | Gradient Operator command.

3. Click on the yellow open folder icon to the right of the Output Grid File, and change the Save as type to DAT XYZ (*.dat) for Surfer 9 or ASCII XYZ (*.dat) for Surfer 8 or previous.

4. Click Save and OK.

5. In Surfer 9 and 10, select the vector map and go to Map | Add | Post Layer. Select the DAT file and click Open (X=Column A and Y=Column B). Use an invisible symbol (if desired) and turn on the labels for Column C (the Z gradient data).

In Surfer 8, go to Map | Post Map | New Post Map. Select the DAT file and click Open (X=Column A and Y=Column B). Use an invisible symbol (if desired) and turn on the labels for Column C (the Z data). Select both the post map and the vector map and go to Map | Overlay Maps to overlay them. 

This method will label every grid node, which often produces too many labels to display. You can set the post map symbol frequency, but it may not be possible to get the data points and labels to coincide with the specified vector frequency, since the vector frequency is set separately for the X and Y directions. There is not an easy way to post the labels only at each vector symbol when the X Frequency and Y Frequency are not set to 1. Some ideas to try:

1. One method is to work with the entire data set as above, and delete points that you don't want to post. You can delete the points from the source data file either manually or in a script. If you use Surfer 9 or 10, it is easy to manually pick points in a post map and delete the corresponding data points from a data file using the View | Track Cursor command. Once the unwanted points are removed from the DAT file, you can reload the data file for the post map and the deleted points are removed from the map.
 
2. Another way is to create points at each vector manually with the Map | Digitize command or with a script. You can then save the XY coordinates of these points to a file. Then use Grid | Calculus to create the gradient GRD file (as above), followed by Grid | Residuals to calculate the Z value of those XY points. Once you have the desired X, Y and Z data, you can create the labeled post map.