From Universe Today:
The numbers are pretty astounding. NASA estimates the galaxy at 100,000 light-years across. Since one light year is about 9.5 x 1012km, so the diameter of the Milky Way galaxy is about 9.5 x 1017 km in diameter. The thickness of the galaxy ranges depending on how close you are to the center, but it’s tens of thousands of light-years across.
If you’re looking for the center of the galaxy, gaze at the constellation Sagittarius, which is low on the summer sky horizon for most northern hemisphere residents. The constellation contains a massive radio source known as Sagittarius A*. Astronomers using the Chandra space telescope discovered why this supermassive black hole is relatively weak in X-rays: it’s because hot gas is being pulled inside the nebula, and most of it (99%) gets ejected and diffused.
Kalirai’s group’s research indicates that the Milky Way formed in the following sequence: the halo (including globular star clusters and dwarf galaxies), the inner halo (whose stars were born as a result of this construction) and the outer halo (created when the Milky Way ate up nearby ancient dwarf galaxies).
Source: Universe Today