It's very simple. Just load in one of your Civ2 maps for instance with the program, then choose "save as bitmap" -and you can save the map as a bmp-file. Then load this in with an image processor (Paintshop) and move around bits etc, cut'n paste etc, save, and then load in the bmp-file with MapEdit -and now you have a grand new version of the old map, that you can save as a Civ2 map-file. You can also create new maps (even oversized) from MapEdit, by typing in the numbers, and then load this in with the Civ2 mapeditor.
You can use the accompanying bitmap to cut out a portion of the map, and then load in with MapEditor, to convert to a Civ2 Map. You have to do a little resizing first, if you want to use the whole map, because it is way to large. Thats why it didn't work out for you.