Engineers build roads from the tile where they begin the turn into the adjacent tile that you click.
First, confirm that the engineer is selected. On the map he flashes with a white outline, and his picture appears in the toolbar on the right side of the screen. To make sure that you are giving an order to build a road, look for a road cursor (a wavy brown line) over terrain tiles adjacent to the selected engineer.
With the road cursor showing over the tile where you want the road to go, click on the map. The engineer moves into that tile and begins working on the road, confirmed by a working animation.
It may take several turns to build the road, depending on the terrain. Flat terrain takes only one turn.
