The order in which the original 13 states ratified the constitution, then the order in which the others were admitted to the union.
Music: Fanfare for the common Man, Dixie, Turkey in the Straw, America the Beautiful.
Since the establishment of the United States, the number of states has expanded from 13 to 50. The Constitution specifies the process by which new states can be added, noting only that "New States may be admitted by the Congress into this Union", and forbidding a new state to be created out of the territory of an existing state or the merging of two or more states as one without the consent of both Congress and all the state legislatures involved.
In practice, nearly all states admitted to the union after the original thirteen have been formed from U.S. territories (that is, land under the sovereignty of the United States federal government but not part of any state) that were organized (given a measure of self-rule by Congress). Generally speaking, the organized government of a territory made known the sentiment of its population in favor of statehood; Congress then directed that government to organize a constitutional convention to write a state constitution. Upon acceptance of that Constitution, Congress then admitted that territory as a state. The broad outlines in this process were established by the Northwest Ordinance, which predated the ratification of the Constitution.
However, Congress has ultimate authority over the admission of new states, and is not bound to follow this procedure. A few U.S. states (outside of the original 13) that were never organized territories of the federal government have been admitted:
Vermont, an unrecognized but de facto independent republic until its admission in 1791
Kentucky, a part of Virginia until its admission in 1792
Maine, a part of Massachusetts until its admission in 1820 following the Missouri Compromise
Texas, a recognized independent republic until its admission in 1845
California, created as a state (as part of the Compromise of 1850) out of the unorganized territory of the Mexican Cession in 1850 without ever having been a separate organized territory itself
West Virginia, created from areas of Virginia that rejoined the union in 1863, after the 1861 secession of Virginia to the Confederate States of America - source Wikipedia/.
Fanfare for the Common Man - (less info) (less info)