Hungary is a Member State of the Schengen Agreement as of 21 December 2007. From that time visas and residence permits issued by one of the Schengen Member States may be used to enter and stay in Hungary, and visas/residence permits issued by Hungarian authorities are - as a general rule - also valid for the entire Schengen Area.
The Schengen regulations are only applicable for a stay not exceeding 90 days. Rules for a stay of more than 90 days are laid down by the national law of the member states concerned.
Citizens of which countries need a Schengen Visa to go to Europe are listed here.
Information regarding visa fees can be found on the website of the Ministry of Foreign Affairs HERE.
For more detailed information please see the official website of the Ministry of Foreign Affairs of Hungary or the Schengen Visa website.