The current organization of the US military has been basically unchanged since the passage of the National Security Act of 1947. This law created a separate Air Force out of the Army Air Corps and changed the name of the War Department to the less-aggressive sounding Defense Department, among other things.
There are FIVE branches of the US military: Army (June 14, 1775), Navy (October 13, 1775), Marines (November 10, 1775), Coast Guard (July 17, 1790), and Air Force (September 18, 1947), in the order that they were created.
The Coast Guard is unusual in that it was, until the last few years, under the Department of the Treasury, not under the Defense Department; instead it was controlled by the Department of Transportation. It was recently transferred to the Department of Homeland Security, along with other government agencies which help protect our home territory and waters, such as the Border Patrol. The Coast Guard is, nevertheless, a military service, and in times of war the president can (and usually does) transfer all of its operation to the Navy for the duration of an actual war.
There are three kinds of categories for military personnel: there are enlisted men and women, warrant officers, and commissioned officers.
Enlisted personnel enlist, or volunteer, for the US military in peacetime. They perform the basic jobs of the military. Enlisted personnel are specialists– they are infantrymen (foot soldiers), artillerymen (shoot big guns), sailors, and so on. In peacetime they serve for an active term that varies according to the service from two to four years. As enlisted personnel move up in rank, they may become “noncommissioned officers,” (such as sergeants) where they command squads or platoons under the supervision of a commissioned officer. In the Navy noncommissioned officers are called “petty officers.”
Warrant officers are very specialized military personnel. They were originally civilians, but after World War I they were moved into the military structure. Here is a valuable link to explain the history of warrant officers.
Below are links to charts that explain military rank (called rate in the navy) and insignia:
Enlisted ranks and insignia –by the way, the letters and numbers at the extreme left of the chart indicate pay rate or grade (E for enlisted, 1, etc., for step on the pay scale). This is useful, because the NAMES of the ranks change across service lines, but the pay rates remain the same.
A good general site to explain the ranks and insignias is here.