To move an existing node in the schematic, merely click and drag the object to its new location. When you move a river node, the river underneath the node will not move with the node. For instructions on moving a river node along with the river underneath, see Moving Multiple Elements at Once below.
You may move a node from one river to another. Because reservoirs can exist both on (river reservoir) or off (local reservoir) a river, you may move a river reservoir off of a river, or a local reservoir onto a river.
For convenience, there is a way to move more than one object at a time. To select multiple objects, hold down the Alt key as you click and drag on the main schematic to draw a grouping box around the intended objects. After a moment, a red box will appear. Click inside this red box and drag to move all objects, including river points.