My advice for the best view of the Milky Way is to go to the Southern Hemisphere. There the central parts of the Milky Way can be directly overhead, and it can really look like a galaxy. So if you are planning a trip down there any time soon, find some time in your schedule to go to a dark site well away from any city lights. It's worth the trip—as a bonus you can also see the Magellanic clouds (the nearest galaxies to the Milky Way).
If you're stuck in the Northern Hemisphere where we see mostly the outer parts of the Milky Way (the center always stays very close to the horizon) you need to find a really dark site, and it also needs to be quite clear. Even small amounts of clouds, through which you can see many bright stars, will hide the Milky Way. Also make sure that your eyes are well adjusted to the dark (stay outside in the dark for a while).
You can use something like Heaven's Above to figure out what time to best see the Milky Way. In the Northern Hemisphere it runs through Cygnus, Cassiopia, and the center is in Sagittarius.
This page was last updated June 27, 2015.