Well, some general advice:

- Rivers tend to start in the mountains and they end up in the oceans.
- Rivers generally don't split as water takes the path of least resistance. There is a notable exception: the river delta.
- Rivers always flow downhill.
- Lakes tend to have an outlet (river) to the ocean as well. A lake can have multiple inlets (rivers) feeding it.

Problems in the map above:
- Some rivers suddenly end on land
- Some rivers split

We have a tutorial about rivers on this forum:
http://www.cartographersguild.com/showthread.php?t=3822