The Milky Way is visible every clear night when the moon isn’t in the sky. However, the Galactic Core is the most interesting section of the Milky Way and it can’t be seen during the Northern Hemisphere winter as the core is below the horizon. The core is visible in the north from March to October, but the best time for viewing it is from late April to late July when it’s visible for longer during the night.

In the northern hemisphere the galactic core doesn't get all that high in the sky, so an unobstructed view of the southern horizon is needed. The galactic core will always be in the southern sky. The free open-source application Stellarium is excellent for showing the Milky Way's location in the sky at any given time.

There are some good websites for how to photograph the Milky Way, but basically this is what they say...


How To Photograph the Milky Way

Requires...
A clear dark sky, ideal on the night of the new moon, but a week before and after a new moon is still manageable.
A digital camera with manual controls (or a film camera if a tracking mount is used)
Manual focus (Autofocus usually won’t work)
Manual exposure
Wide angle lens (28mm and wider is best)
Remote release or self-timer
A tripod (ideally, with a tracking mount), or
      Keep exposure as short as possible to limit star trails (15 seconds, no more than 30)
      Highest usable ISO
      Fast lens (f2.8 or faster)

Also...
Sensor size as large as possible
Headlamp (LED headlamp with a red “night vision” mode preferred) or Flashlight
Enable long exposure noise reduction
Auto White Balance