Updated : 26/04/2017
As an EU citizen, you don't need to report your presence upon arrival in Hungary.
You must however, register your residence if you intend to stay in Hungary for more than 3 months. You must do so within 93 days of arrival.
To register your residence you should go to the Office of Immigration and Nationality or its regional directorates.
When registering your residence you are required to present a valid travel document or personal identification card, and the documents proving your right to stay in the country (such as proof of paid activity, studies, financial conditions necessary for living in Hungary, health insurance, residence).
For more information, check with the office for Immigration and nationality.