The First Flag
The U.S. had no official national flag at the time of the signing of the Declaration of Independence on July 4, 1776. The origins of the flag are unclear.
Where did the design come from?
According to one theory, it is based on George Washington's coat
of arms. 
Another theory states that the flag is based on a design by the Sons of
Liberty, which has 13 alternating red and white stripes. Francis Hopkinson
may have designed the flag. He sent a bill to Congress for his work,
requesting a "Quarter Cask of the Public Wine." He never got his payment, but
no one contested his claim to have designed the flag.
Who sewed the first flag
It is popularly believed that Betsy Ross sewed the first flag, after a sketch by
George Washington, who personally hired her for the job. However, some people
think that Rebecca Young did. Incidentally, her daughter, Mary Pickersgill, made
the flag that flew at Fort McHenry and inspired our
national anthem.
The Flag Resolution
On June 14, 1777, the Second Continental Congress passed the Flag Resolution,
which established the first U.S. Flag. The resolution read:
"Resolved, That the flag of the United States be thirteen stripes, alternate red and white; that the union be thirteen stars, white in a blue field, representing a new Constellation."
The Resolution didn't specify an arrangement for the stars. The flag that
was used in the early days had the stars arranged in a circle and is popularly
known as the "Betsy Ross" flag.