How can I make a terrain generator that makes more realistic terrain?
My current generator makes this type of terrain:

how can I make it make more real terrain, like lakes and rivers?
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Basically you define and apply a set of filters on your generated terrain.
I can’t go into full detail but I’ll provide some hints for you to google:
For rivers you could create a voronoi diagram that has thin dark lines between the light cells. You could have some gradient from dark to light for smooth transitions. Then you mulitply that diagram with your generated terrain effectively lowering hight along those lines. Together with the irregular shape of your terrain you could get some non-straight “proto”-rivers.
Next you could apply an erosion filter that simulates rain, water flow and erosion to get more realistic and smooth rivers and lakes.
This should get you started.
For more information pay VTerrain.org a visit, for example this page: http://vterrain.org/Elevation/Artificial/, or this for water simulation (hydrogeology): http://vterrain.org/Water/index.html#Hydrogeology