an understanding of herself and the role she wants to take in society and her life, there is no need to be preachy.  In fact the play's more dramatic scenes are best done quietly.  In order to best relate with modern day women, it would be best to have the actors and actresses involved talk with psychiatrists regarding controlling and psychologically abusive relationships. The actress playing Nora would also benefit from talking with a woman who has made a similar decision to walk away from her marriage in order to "save herself." 

The choice to leave the children with the husband seems as shocking today as it did in the Victorian period (especially if Torvald is portrayed as psychologically abusive and overly controlling).  Nora, in the Victorian period, was viewed as selfish and a bad mother for leaving her children, according to the critics of the play.  In the modern version, this choice would have to be handled carefully, at the risk of Nora being vilified for leaving her children with an abusive monster.   However, it does bring up an interesting possibility for the play.  If the play were to be gender swapped, the only way for the male version of Nora not to come off as a deadbeat would be to take the children with him when he leaves.  This entertains a unique discussion that falls in line with Ibsen's initial points when the play was first produced.  The question is if a man is in a psychologically abusive relationship, does he have the same rights to leave the woman?  And what are his responsibilities regarding the children who, if left, will be in danger of the same abuse?  Is he a deadbeat or is he simply standing up for himself?  These questions were applied to Nora as the door closed at the end of the play and created a great deal of turmoil with critics, religious groups, and especially in the news and with the general public.  It can be assumed a modern approach to the play would bring about similar results.

My first reaction is to problematize the notion of "relevance." There is no real reason that people should only experience things that are familiar and comfortable. The point of reading or watching plays from other eras is precisely to learn about people who have different belief and lives than we do. Thus in terms of staging, I think accurate historical reconstruction is a good way of letting the audience get a sense of experiencing something fundamentally different than the social media and local bubble of their daily lives. Thus I'd avoid a translation that used 21st century slang and instead look for a 19th century translation to emphasize that this is not a 21st century drama.

As part of this aims to make a production as much of a valuable experience of difference as possible, I'd avoid the tendency to make Nora a contemporary independent woman or an unambiguous heroine, and perhaps see if Torvald Helmer can be played sympathetically, so that the play becomes more about tensions in a marriage and the problems of deceit than simply the triumph of Nora in becoming an independent woman. Traditional proscenium staging, perhaps with a thrust, works well to give a sense of the respectable middle class setting which is such an important element of the play. 

A Doll's House doesn't need a contemporary adaptation in order to be relevant to a modern audience; its themes already create the relevance.  Torvald's unwillingness to take Nora seriously and his shame in her efforts to save his life resonate with issues today in which women's concerns are minimized. 

Nevertheless, almost any good drama with universal themes can be adapted and given a more contemporary look.  You could begin with costumes and setting.  Other than the fact that they have household help, the Helmers are not much different than modern middle-class couples.  Make their home a contemporary home with a television and a computer, and dress the Helmers in modern clothes and you've already hinted to the audience that their problems and issues could happen today.  And the nurse could certainly be a modern-day "nanny" wearing casual clothes instead of the rigid uniform of the late nineteenth century. 

Another way to adapt a drama to a contemporary setting is to use current music playing in the background and as the curtain rises.  A clever director might look for songs that suggest some of the same themes as the play.  Other stage elements such as lighting can enhance the contemporary setting, and the acting could play up the relationship among the characters in a more modern way.  Even props around the house can indicate a contemporary lifestyle, such as current books, shopping bags from stores, and other accoutrements of modern life.

A New York Times review of a 2010 production (see link below) gives examples of just such contemporary touches; the article lauds the changes and describes their impact on the audience.

With so much negativity about child abuse and abandonment nowadays, perhaps employing the alternate ending of Ibsen's play in which Nora does not leave her children would better satisfy audiences.  Certainly, Nora can more easily leave Torvald and take the children along with a modern audience viewing, although her doing so may compromise the realism of the play for its time period.

Retaining the costumes of the time is important for the realistic aspect of Ibsen's play. After all, the problem of patriarchy and the femme covert laws is clearly within the Victorian Age, so depicting it through costumery is essential in order to convey this time period in order that audiences will accept the situation.  These same audiences are less likely, however, accept other realistic aspects such as Nora's leaving behind her children.

If you want to "contemporarize" the play, you might change the clothing to better represent the contemporary upper-classes, as suggested above. 

I agree also with the opinion that this play's commentary and subject matter remain relevant today and the text of the play seems perfectly understandable now.

Perhaps one exception is the inherited spine disorder of Dr. Rank. This doesn't make much sense to today's understanding of heredity, or at least his explanation of it doesn't. He believes that rich foods and "high living" on his father's part have given him a spine disease.  This could be adjusted, but doesn't need to be in order for the play to be relatable.

It seems the message ofA Doll's Houseis universal and immortal enough that the dialogue and relationships carry it in any era yet known to experience. Therefore one might change the setting, e.g., furniture, wall hangings, and the costumes, e.g., contemporary upper class clothes, without compromising the integrity of the play and its message. However I think changing the social class in which the action occurs would compromise the integrity of play and message.