Here is some advice for completing your assignment of finding ten to fifteen quotes and analyzing them!
First, let's identify what some of the major themes of the play are. As the title suggests, youth versus age is an important theme. The passing of time means aging, which is a big worry for these characters. As Hollywood actors, their work is influenced by their looks, and therefore youth is important to them.
Sex is another theme present in the play. Sex becomes part of Chance's job, as he makes money through offering sex and/or companionship to women. Princess Kosmonopolis feeds into this as one of Chance's customers. Boss Finley has a younger mistress. Sex influences relationships and the characters' lives.
Other themes include escapism, as Princess Kosmonopolis engages in sex and drugs to run away from her everyday life, and hypocrisy, as demonstrated by Boss Finley.
With these themes in mind, we can look for quotes that might demonstrate them.
One that I found is this quote from Heavenly:
Scudder’s knife cut the youth out of my body, made me an old childless woman. Dry, cold, empty, like an old woman.
Heavenly has a hysterectomy because of the sexually transmitted disease Chance passed on to her. The operation has left her sterile. This quote is connected to the theme of sex, as the consequence of Chance's encounters with other women has led to the disease. It is also connected to the theme of aging, as Heavenly claims the operation "cut the youth" out of her and effectively aged her.
Time—who could beat it, who could defeat it ever?
The above quote from Chance is connected to the passing of time. Chance is distressed at the idea of aging and losing his youthful looks.
When you find your quotes, you can analyze it by restating it in your own words, explaining how it is connected to a theme in the play, providing explanation of the context of the quote, and identifying any figurative language present.
I hope this helps you complete your assignment!