The Milky Way is a barred spiral galaxy estimated to be somewhere between 100,000 light years and 180,000 light years in diameter, containing an estimated 200 billion to one trillion stars and at least 100 billion planets. The center of the galaxy is likely a super-massive black hole.
As exploration of the galaxy expanded the knowledge of several species, it became clear that some very ancient species had influenced the destiny of the galaxy. These species included the Xel'Naga.
Stellar cartographers ultimately divided the galaxy into four quadrants - the Alpha Quadrant, Beta Quadrant, Gamma Quadrant, and Delta Quadrant. Some other areas concerning the star charts of the galaxy have been labeled as quadrants as well -- although these are hotly debated and are not recognized by the United Federation of Planets. These include the Theta Quadrant -- which is the center of the galaxy -- and the Sigma Quadrant, which is a region just outside the borders of the galaxy. The galaxy is further sub-divided into sectors, star clusters, planetary regions and star systems.
The Milky Way has long been home to a myriad of cultures and factions. For much of its history, however, an interplanetary government has emerged -- covering at least large portions of the galaxy in its territory. Deep in the Delta Quadrant, this was the Peacekeepers for many cycles. Even longer than that, the Citadel held sway over most of the galaxy. After this, the United Federation of Planets became the primary interplanetary government.
Although there are numerous other galaxies in the universe, and others even relatively nearby the Milky Way in what is called the "Local Group", only a few species from other galaxies had been encountered by any of the species within the Milky Way even by the year 40,000.