To create a road, right click on the hex where the road is to begin. In this example, the road will be a continuation of a previously existing road

Then, left click to the hex the road will extended to.

Continue to left click to new hexes until the road is complete

To turn off the road drawing, just left click on a non-adjacent hex

To erase a road, right click on the hex where the road erasure is to begin.

Then, left click the adjacent hex with the road the connecting road. The road connection between the hexes is then erased.