Instructions
Evaluate the type of map you have. Some types of maps make flow direction very easy to determine. It is easiest if you have a topographic map, with printed elevation contours--the water flows from higher elevation to lower. There are other methods for other types of maps.
Follow topographic contours that cross the stream. All contours that cross a stream valley bend uphill as they approach the stream. The result is a V shape that points upstream. The contour and the line of the stream make a sort of arrow that points opposite the direction of flow. If the map does not have contours, observe the pattern made by all the streams on the map.
Trace the pattern formed by the creek and all creeks that join it or that it joins. Most patterns look like a tree, with branches that form Y and V shapes where they join. The Y and V shapes point in the direction that the streams flow. If the streams don't form a tree shape, there are still other methods.
Look for other clues. Almost all streams become larger in the direction the water flows, so if the line marking a stream ends without joining another stream, it is most likely the upstream end of the creek. This is especially likely if the line ends at a spring or a small natural pond.