In 1753 “An Act for the better preventing of clandestine Marriages” set forth the rules for being married by the reading of the banns or by a common license, including the method of procuring either of these licenses. Most of Jane Austen’s characters would have used a common marriage license as it lacked the public nature of the banns and was easily available to the gentry class.
Under the Act, assuming that their were regular church services held in the parish in which the bride and/or groom lived, procuring a common license was primarily a question of paying a fee; having either the bride or groom live in the parish for at least four weeks before the wedding; and ensuring that a bride or groom who was under 21 years of age either had permission from their father/legal guardian or was a widow/widower.
The Act states that if there were not church services regularly held in the bride or groom’s parish, an adjoining parish could be used.
 I have read that by the time Jane Austen’s novels were published that the English courts had ruled that a mother had the right to be her child’s guardian if her husband/the child’s father was dead. I have not however been able to find that ruling.
Updated October 18, 2015