Option 1: Edit the grid to remove all data greater than or less than the desired threshold.  This will work for any grid based map layer. Let's say you want to color only the areas of the map where the Z value is less than 150 (so all areas where Z is greater than 150 are transparent). To do this:

1. Click Grids | Calculate | Math.
2. In the Grid Math dialog, click the Add Grids button, select the grid file and click Open.
3. Enter the function: IF (A>=150, 1.70141e+38, A). This tells Surfer that if the Z value in the grid is greater than or equal to 150, then convert it to the Surfer NoData value (1.70141e+38), otherwise leave the Z value alone.
4. Enter a new Output Grid name and click OK to generate the new grid.
   
5. Create the map from the new grid.

Option 2: Edit the colormap to apply a 0% opacity to all values above or below the desired threshold. This will work with contour and color relief maps. Let's say you want to color only the areas of the map where the Z value is greater than 50 (so all areas where Z is less than 50 are transparent). To do this:

1. Click the Contours layer in the Contents window to select it.
2. Click the Levels tab in the Properties window.
3. Click the ellipses  button in the Fill colors field.
4. In the Opacity Mapping section of the Colormap Editor, click in the Presets field and select Middle Ramp.
5. Click the second node in the data histogram and enter the desired threshold value in the Data Value field.
6. Repeat step 5 using the same value for the third node.
   
7. Click OK to apply the colormap and close the Colormap Editor.

Option 3: Set the minimum contour to the threshold value.  This will only work for contour maps where you want to fill the map above the threshold value.  Let's take the above example where you want to color only the areas of the map where the Z value is greater than 50 (so all areas where Z is less than 50 are transparent). To do this:

1. Click the Contours layer in the Contents window to select it.
2. Click the Levels tab in the Properties window.
3. Enter 50 in the Minimum contour field.
   

Updated November 24, 2021