Several things can or will happen:
First of all, you become single again -- you are no longer married. You can date, get remarried or stay single. You can file your taxes as “Single” (or, if you have dependents living with you, as “Head of Household”) rather than as “Married.” Usually the ex-wife can also resume the use of her maiden name – and often this may be requested in the divorce papers that are filed by her.
A divorce, however, doesn't necessarily mean that child support, alimony, property division and custody are all resolved. This depends on the law of the particular place (state or country) where you file for divorce or dissolution of marriage.
In the United States, that's what must happen before the divorce is granted; all issues in dispute between the parties must be resolved by trial (and all not in dispute must be settled by written agreement) before the court will give you a divorce.
In the Russian Federation, however, the divorce may entirely separate from these other issues and may be granted independently of a resolution of these issues; you can go ahead and litigate (fight in court) any contested issues at any time before or after the divorce, which is granted independent of the claims for property division, custody, child support and spousal support.