Orient the map towards true north. Do this by looking for the four-pointed compass symbol that is usually in the top corner of a map. Line up the north part of the the compass symbol with the magnetic north end of your hand-held compass. This will give you a close approximation of north, which is all that is necessary for this project.
Look on the map for the different bodies of water. They should be colored blue. The Nile should not be hard to find because of its size, but in some places, where it is dammed or naturally very wide, the big river might resemble a lake. Because of its size the Nile should be labeled, but it is also possible that the river night have different names or be referred to as a lake, if a dam is present.
Look for contour lines that cross the river. When you find one, write the number of the contour in the middle of the blue area with your pencil. Be aware that your elevation readings will likely be in meters instead of feet. After you have recorded several numbers close together, draw a line that begins with the higher numbers and heads to the places of lesser value. At the end of this line make an arrow by adding a V-shaped mark to the end of the line, so that the line is now pointed in the direction of lower integers. This is your downstream direction.
Test your calculations by tracing contour lines as they cross a river or stream. Do this for a little ways on both sides of the body of water. A flowing river should create many rows of V marks with the tip of the V being located on the river. The tip of the V will always point downstream.
Erase all pencil marks and numbers after you are done.