I don't have much to offer in the way of science, just my own way of doing it. I start with a general layout with a fat 19 pixel tip and then I just find a deep bay and start a river there. I keep to the the valleys and plains and rough in the main channel and major branches in straight lines. Lower the opacity, make a new layer, zoom in (so that I can see the lay of the land) and grab a 5 pixel tip and then I go back over the layout for a ways (starting at the coast) then switch to a 3 pixel tip and make some branches. I do the smaller rivers in a 1 pixel tip and put a lot of those in. What I end up with looks similar to a tree or lightning bolts, but a lil smoother on the squiggles and less jagged. Finally, I use the smudge tool on the ends to fade them off into the distance.
Every river that I draw gets at least 2 branches or else I'm not drawing it...it will just be one single squiggly line and that looks odd to me. For every major river (5 pixel) I put in at least 4 minor rivers (3 pixel) and 8 small rivers (1 pixel) that connect to the coast...that way they aren't all the same size at the delta. I also make sure that the rivers have a varying width, skinny parts and fat parts...looks a lil more realistic to me and a tablet is a big help there. I'm not afraid to have straight areas so long as I have enough loopy parts (big wide bends) to counter-balance them.
If I feel that there are too many then I go back and start erasing but I tend to not erase enough and always have lots of rivers. My river systems aren't technically correct...just what I think the water will do. For me it's about getting the aesthetics right and not worrying too much about the science.