Attention: Please refer to Alim Deen for Authentic Details, This answer just gives basic guideline and concepts -
Divorse in islam is 'The Most Disliked -Permissable Act'. If Husband and wife can no more Follow the commandments of Allah while living together, then they have an option to separate. When the husband gives 'Talaq'(Divorse) 1st time, It is possible for them to reconcile, If the husband gives Talaq 2nd Time, still they can reconile and agree to live together. But if husband gives Talaq Third time, then Husband and wife can no more live together under one roof. They are Haram on each other. They must seperate.
If required by wife alone and husband is not willing to give talaq, she can go to court of law and file a case for 'Khula'(Divorse). The court after reconcilation efforts,issues the separation orders.