The steps are:

1. Create the post map in the plot window.
2. Click File | Open in Worksheet, select the data file and click Open. It will open in the worksheet window.
3. If the X and Y data columns are not columns A and B in the worksheet, click Data | Data | Assign XYZ Columns to assign the correct columns to your X and Y data columns.
4. Click View | Windows | Tile Vertical to arrange the windows next to each other.
5. Click Map Tools | Layer Tools | Track Cursor to enable cursor tracking.
6. Click in the plot window near a point, and that point is highlighted in the worksheet window.
   
7. Click in the worksheet window and edit or delete the point.
   
8. Then click back in the plot window near your next point. Repeat.
9. When finished, in the worksheet window you can click File | Save to save the edited data (or File | Save As to save it to a new name). Click File | Close to close the data file.
10. To update the post map, from the plot window, click File | Reload Map Data. If you wish to update a contour map with the edited data set, you must regrid the data (Grids | New Grid | Grid Data) and then update the contour map with the new grid file.

In Surfer 14 and newer, a data file can be also be edited by creating a base map from the data file data. For additional information about this process see the article I want to extract all of my post map points within a polygon on my base layer. How can I do this?

See also: What Is Surfer's Track Cursor Command?

Updated November 2, 2018