What is the climax of this play and how can Blanche, Stanley, and Stella be described with only few words? Who can give me a brief, but...

In Tennessee Williams "A Streetcar Named Desire," the major conflicts of the play revolve around Stanley Kowalski.  First, he is displeased that Blanche DuBois, sister of Stella, has come uninvited to live with her sister.  Next, he perceives that she has set up a screen between the reality of her leaving Belle Reve and what she purports.  Then, he becomes somewhat possessive of Blanche as a member of his home and resents his friend's, Mitch's, attentions towards Blanche.  These conflicts, which also represent the conflicts between the industrial Northern culture and the aristocratic Old South, come to a climax when Stanley's anger turns to physical violence and he rapes Blanche.

With the theme of class conflicts, Stanley represents the unrefined, uneducated, somewhat brutish immigrant who is part of industrial America.  Blanche and Stella, on the other hand, represent the female aristocratic tradition of the Old South challenged by increasing demands for man-power in the industrial cities.  Representative of this theme of class conflicts are Stanley's references to his courtship of Stella:

When we first met, you and me, you thought I was common.  How right you was, baby.  I was common as dirt.  You showed me the snapshot of the place with the columns [Belle Reve*].  I pulled you down off them columns and how you loved it.

Thus, the characters of Stanley, Stella, and Blanche, rather than being well-drawn characters are representative of types.

* Belle Reve (French) significantly means beautiful dream. Blanche resides in a dream world as she cannot deal with her personal conflicts.  On the other hand, Stella returns to Stanley at the end of the play to "go on living" as Tennessee Williams wrote.  She faces life and deals with it, rejecting her sister's delusions of living in the past.