Here a good example and tutorial from youtube for watershed delineation and river formation using digital elevation model (DEM).

The steps as follows:

Watershed delineation
1. Spatial analysis tools
       -> hydrology
            -> fill
            -> flow direction
            -> flow accumulative
            -> basin (using input from flow direction)
2. Conversion tools
      -> from raster
            -> raster to polygon (using input from STEP1-basin)
Clip the selected watershed
3. Geoprocessing
      -> Clip (select watershed that want to clip)
River formation
4. Spatial analysis tools
      -> map algebra
            -> raster calculator
                  -> flow accumulative > 500 (value is example)
                  -> flow accumulative > 1000 (value is example)
5. Conversion tools
      -> from raster
            -> raster to polyline (using input from STEP 4-flow accumulative>1000)
                  -> Clip
Clip the DEM raster
6. Data management tools
      -> raster
            -> raster processing
                  -> clip (input (raster), output extend (basin, STEP3), click used input feature for clipping                         geometry)