No typically a divorce is not granted right away. The Court procedures for conducting a contested divorce takes approximately 9-12 months, which means that the combined time until the divorce will conclude can be as long as two years from the date the parties separated.
If parties can resolve all marital issues and property by agreement, the parties can then proceed with an "uncontested" divorce. The Court procedure for this is simple, quick (often less than 90 days) and relatively inexpensive.