Using health and Nike+ ipod app
If you're using an iPod (e.g. nano as I do), then the trainings won't be synced to Health App. Otherwise using Nike+ Running App your runs will be automatically synced with Health App as far as you added Running App as a source in the Health App.
What I personally find disappointing, that Nike doesn't take a use of a step counter of an iPod and leave all the data on the iPod.