Jane Austen actually does not give very many descriptions for her characters. She prefers far more subtle characterization techniques, such as dialogue.

However, one character that is described is Elizabeth. We learn in the first chapter that her father believes she is more intelligent than her other sisters. We learn at the Meryton ball that she has a "lively, playful disposition, which delighted in any thing ridiculous" (Ch. 3, Vol. 1). Concerning her looks, we know that Mr. Darcy thinks her "dark eyes" possess a "beautiful expression" (Ch. 6, Vol. 1). We also know that he thinks her figure is not perfectly symmetrical, but that it is "light and pleasing" (Ch. 6, Vol. 1). Elizabeth is also acknowledged as the second most beautiful Bennet daughter next to Jane (Ch. 15, Vol. 1).

Jane is acknowledged to be the most beautiful daughter (Ch. 1, Vol. 1). She is also described as having a very naive and trusting character. She is very quick to accept everyone as wonderful and dismiss their faults (Ch. 4, Vol. 1).

Mr. Bennet is described as being intelligent, having a "sarcastic humour," "reserved nature," and also as having "caprice," or an unpredictable nature (Ch. 1, Vol. 1).

Mrs. Bennet is described as understanding little, knowing little, having an "uncertain temper." She also  always "fancied herself nervous" (Ch. 1, Vol. 1).

Mr. Darcy is described as very tall and handsome, but also as very proud (Ch. 3, Vol. 1).

Austen also feels that Mr. Collins merited physical description. He is described as being tall, but also very "heavy," meaning obese (Ch. 13, Vol. 1).

Another character's description that is worth mentioning is Charlotte Lucas's. She is described as being plain and already 27, two reasons why she accepted the proposal of Mr. Collins (Ch. 22, Vol. 1). She is also described as being "sensible" and "intelligent" (Ch. 5, Vol. 1).

A complete index of all the characters in Pride and Prejudice and their descriptions can be found in the link below.

How does Jane Austen deal with gender and character in Pride and Prejudice?

In Pride and Prejudice, Jane Austen uses gender and character to both express the social norms of her time and to emphasize that there are more variations on character than society chooses to recognize. The Bennett sisters define the whole of female society. There is Jane, the incomparable beauty, who should be able to secuure a worthy suitor without ever opening her mouth.  Then there is Elizabeth, very intelligent, independent and quick witted.  She, it is thought would not secure a eligible suitor, her beauty being average, once she opened her mouth, men would run away from her fierce opinions and strong mindedness.  Lydia, a silly girl given to spontaneous decisions fell into trouble, she should have been watched more closely by Mrs. Bennett, who is a caricature rather than a real mother.  Mary, the studios one, will never marry and Kitty, too young, but expected to be able to secure a husband of some means.  Mr. Darcy is the rich, indignant, handsome, austere gentleman who one would never expect to find Elizabeth Bennett attractive.  You expect him to choose a wife based on social standing and breeding alone.  Bingley, although not as rich as Darcy, but still well off, is looking for love.  Mr. Wickham is a cad and a rouge, who is looking for a wife who has a rich purse.  Mr. Collins, the minister, needs a wife, any wife. Jane Austen paints her characters in broad strokes.   

How does Jane Austen deal with gender and character in Pride and Prejudice?

This question could take pages to answer, but I will focus on the Bennett family to give you a brief look at how deeply gender and characterization are dealt with in this novel. Austen depicts Elizabeth as a bold, intelligent woman who easily and openly expresses her opinion on various subjects from marriage to family. However, Elizabeth's mother and younger sisters tend to fall into the stereotypical feminine role during this time - meaning that they were more concerned about appearing beautiful and important and impressing others than truly making themselves happy. Elizabeth's older sister wishes she could be more like her determined sibling, but she too is unable to articulate her feelings as easily as Elizabeth. In the end, the girls all find some sense of happiness - thanks primarily to Miss Elizabeth Bennett.

How does Jane Austen explore relationships in Pride and Prejudice?

Austen strategically matches each couple by issue, personality, and mannerism in a way that stands out almost as if scientifically planned. Her relationships in Pride and Prejudice are like formulas that, when combined, form interesting reactions.

In the case of Lizzie, we know about her behavior through her actions and through her words, but as far as feelings go, she leaves us wondering and waiting for her to say big words, which she doesn't.

Darcy, her counterpart is the same way. All we know of him is through his actions and words, but both Lizzie and Darcy are too much complex of characters for us to expect them to form a romantic bond. They did, however, and, in the end, we still are left wondering "how did it happen?"

Charlotte and Collins are the joke of the story. Collins is into himself so he needs someone who is GOING to be into himself. Lizzie rejected him and his ego, so his most logical shot would be the plain and empty headed Charlotte, who even admitted that this is a good move for her to do in order to make herself somebody.

Bingley and Jane, both quiet, both unsuspecting, both going with the wave, got together in what one could consider far from a passionate romance, a soap-opera type encounter. Bingley and Jane really do not make too much noise in the story.

Wyckham and Lydia however do make up for all the noise Jane and Bingley left behind. These two were an ill match made on purpose to show the weaknesses of an ill breeding on the side of the Bennets. Lydia, a ticking time bomb, fell for Wickham's uniform, more than for the soldier inside of it. Wickham is as shallow and libertine as anything, so he eloped with her, ruining her reputation in society. Both still careless, Darcy intervened to provide money to marry them off for the sake of the Bennets reputation (and knowing now that Jane was his friend's love interest), and had them return to society. Lydia still clueless, Wickham, still shallow.

No relationship experiences dynamics for Austen, as they remain the same sentimentally, but once their characters are put together, the readers can see how they matched strategically from the beginning.