If you normally eat a good, nutritious, balanced diet, you don't need to do anything special before or after an average run. You don't have to be concerned until you get into much longer or harder workouts.
My general rule of thumb is eat what your body wants, errr, of course within limits. It seems like in the winter time my body wants asparagus and either chili or BBQed chicken thighs, but in the summer time, especially after a long run on a hot humid day, my body wants milk and cookies. In the spring and fall, beer looks especially good after a run.
Fat old man PRs:
I agree with the previous posts but when I'm training hard, I know my nutrition seems to suffer. After a hard or long run I try to eat a Recovery Bar because I know you need a certain ratio of carbs and protien. PowerBar has some really great tasting recovery bars so that's my go to.
My response would be "it depends...." It depends a lot on your personal metabolism and nutritional needs.
In general, I find that I need protien after long runs to help my legs recover, so I tend to dose up on that. Otherwise, a generally balanced diet of protien and carbs does well for me. But here is my general post run meal plan:
(I'm a morning runner, so everything I note here is geared towards morning type foods)
If it's a short run, say under 6 miles, I look for something that is a combination of protiens and carbs, but not too much in volume. I tend towards cereals or yogurt with blueberries or strawberries.
Between 6 and 10 or so miles I'll start looking at eggs, like at least four of them, with cheese, and whole wheat toast. Maybe throw some ham or turkey in with it.
For 11 miles and beyond, I'll start with a protien-banana shake and follow that with eggs or perhaps a turkey/cheese/lettuce sandwich.
For the long-long runs, like 18+ I'll always do the protien-banana shake first and then eat more later. After these longer runs, I tend to eat smaller portions but somewhat frequently.
Hope that this is helpful -