Follow the first rule of hydrology: liquid water flows downhill by the steepest gradient available. If there is only uphill (as happens in a basin), then water will fill the basin until it finds a way to go downhill again. Repeat application of the first rule as required until you've identified all of the downhill, with the edge of your map generally being treated as a really big downhill drop. Areas converted from basins to filled areas will be lakes.
There are, of course, always some hidden ideas in there, namely that water frozen water generally doesn't flow, liquid water won't visibly flow if it's below ground, and water can evaporate into vapor if conditions are correct. Surface flow may also appear intermittent depending on local conditions. Water may flow into a hole and never reappear or just appear out of a hole and go merrily across the landscape (common in karst terrains). Water may start out frozen as a glacier, thaw into a river, and disappear into desert sands (common in interior deserts). Water may flow in fantastic loops and bends across nearly-flat terrain if it has no other way to balance its energy budget (see your favorite meandering river). Rivers may split apart into lots of smaller channels if conditions are right (anastamosing river). But the first rule continues to apply!
Your maps seem to have a recurring "feature" in the form of little basins where rivers join. If water were flowing downstream, those basins would be filled with lakes. Some hydrology sims (e.g. Wilbur) have this misfeature due to how downstream flow is calculated and applied. It can also occur in real-world DEMs that are undersampled because a relatively narrow gorge at an unfortunate angle can be sampled as a saddle next to a basin, which isn't hydrologically accurate. If you've got a set of vector contours, it can be easier to dispose of the little pits than it is to draw lakes everywhere. Some programs (again, Wilbur is an example with which I am familiar) have an option to fill basins or to fill basins as lakes and either of those options will take a lot of the drudgery out of the work.
I marked up some of the places that are likely to be lakes in your example map:
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