A road is considered complete with it stops on both ends. Roads always end at a castle, and at a crossroad.
A Cloister is considered complete when there are 8 tiles immediately surrounding it, so that it is in the center of a 3x3 square of tiles.
In this picture, the cloister in the center of the picture is finished, but the two right next to it are not because they have some tiles missing. The road coming from the completed cloister is also complete, because it ends at a city.
A completed cloister scores 9 points (1 for the cloister tile and one for the 8 tiles that surround it). At the end of the game, an uncompleted cloister scores 1 point for the cloister tile and 1 point for every tile that is surrounding it.
A completed road (or uncompleted, at the end of the game) usually scores 1 point for every tile the road is on (if your road loops back on itself, you don't count the start tile a second time).
The exception to this rule is if you are using the Inns and Cathedrals expansion. This expansion comes with some tiles which contain an "Inn on the lake" (in this picture, there is one in the bottom middle, on the tile containing part of a city). In this case, if your road includes one of these tiles,a complete road counts 2 points per tile, and 0 points if it is incomplete.
