To answer this deceptively simple question, I referred to the Longman Dictionary of American English and also asked a number of native-speaking friends and colleagues. Below is a list of examples plus a summary.
1. a female child: tall for a girl her age | when I was a little girl | girl clung to her mother’s dress
2. a daughter: We have two girls and a boy.
3. a newborn child: It’s a girl!
4. a woman’s female friends: I’m going out tonight with the girls. | Let’s go, girls!
5. informal encouragement/approval for any female: You go, girl! | Atta girl! (= That’s a [good] girl!)
6. girlfriend: She’s my girl. (old-fashioned)
7. name for employee: the girls working in the office (old-fashioned, considered offensive or sexist by feminists)
8. weak person: You throw like a girl. (derogatory)
9. a gay male (spoken by another gay male): Hi, girls!
10. female solidarity: Hillary Clinton’s my girl!
1. woman, esp. to be polite or if unknown: the young lady working behind the counter
2. woman with a strong character: She can be one tough lady to negotiate with!
3. unfamiliar woman (impolite, spoken): Hey, lady, get out of my way!
4. a formal or polite adult female: behaves like a lady
5. wife of a British Lord or Knight: Lady Wimbledon
6. formal address: Welcome, ladies and gentlemen, to our annual event.
7. civil or friendly address: Good evening, ladies. Can I bring you a drink while you’re looking at the menu?
8. a girl: (used by someone in authority): Where do you think you’re going, little lady?
1. an adult female: the woman I was talking to | a married woman | women’s clothing department
2. a profession or job: saleswoman, chairwoman, spokeswoman, businesswoman, congresswoman
3. a medical reference: a 20-year-old woman with headaches | a procedure for any woman over 50
4. patronizing speech from a male adult: Woman, bring me another beer! | What you talking about, woman?
5. an old woman is someone who is facing health/physical challenges
As can be seen above, there are many specialized uses. The comments in this paragraph refer only to chronological (age) assignments. As a rule of thumb, use “girl” for any female up to college age, use “young woman” until about 30, and use “woman” after 30. “Young” can be added depending on the age of the speaker. “Old” is not really appropriate; instead, give the female person’s age if it is relevant to your story. Sometimes the distinction between “girl” and “young woman” depends more on perceived maturity and less on actual age.
For feminists (especially many native English speakers who lived through the 1960s and 1970s women’s movement), the term “woman” is preferred in everyday speech over “lady” to designate an adult female. First, it is the linguistic counterpart to “man.” Second is the perception that “lady” has classist and sexist connotations; to them, a “lady” represents an inconsequential female of no personal accomplishment (other than connection to nobility). Here, the assumption is that any female who can compete head to head with a man should have the parallel expression of “woman.” Older Americans of both genders who do not identify with the women’s movement or notions of legal/financial/political equity tend to use the term “lady,” including expressions which “mark” (and therefore diminish) the professional stature of trained females: lady doctor, lady mechanic, lady pilot, lady engineer. This group may also include speakers of lower education or more rural status who identify female office workers as the “office girls” (even though they would never say “office boys” to identify the males who work in the office).
If a female is unfamiliar, a public reference to her as “lady” may feel more polite: the lady who dropped her purse | This lady was ahead of me in line (so please wait on her next).
Note the paired human expressions below.
MALE / FEMALE (NOTES/MEANINGS)
Man / Woman (An adult person)
Gentleman / Lady (A formal expression)
Lord / Lady (Titles of nobility)
Boy / Girl (Youth)
Guy / Gal, Girl (Informal titles)
Dude / Chick (Slang titles)
Actor / Actress (Modern usage favors “actor” for both genders.)
Steward / Stewardess (Unless necessary, use “flight attendant.” )
Male nurse / Nurse (Modern usage uses “nurse” for both.)
Chairman / Chairwoman (May use “chair” or “chairperson” )
Note the old-fashioned referents which implied all people or a particular gender and their more modern substitutes.
OLD // MODERN-NEUTRAL
man // person
men // people
everyman // everyone
mankind // humankind
kingdom // territory
he // he/she, s/he, one, they
his // his/her, one’s, their
policeman // police officer
fireman // fire fighter
mailman // letter carrier
cleaning lady // housekeeper
God/he // God/God
secretary // office professional (O.P.) or assistant
workmen // workers
Note the paired animal expressions below.
MALE / FEMALE / NAME WHEN GENDER IS UNIMPORTANT
sire / bitch / dog
tomcat / she-cat / cat
fox / vixen / fox
tiger / tigress / tiger
lion / lioness / lion
ram / ewe / sheep
boar / sow / pig
buck / doe / deer
bull / cow / cow
stallion / mare / horse
rooster, cock / hen / chicken
drake / hen / duck
gander / goose / goose
tom / hen / turkey