Are you planning to work or study in Belgium for more than three months?  If yes, then you need to get a permit to live in the country legally.  Getting legal residency will be a lot easier for you if you are an EEA national.  EEA stands for the European Economic Area, and it includes the European Union countries as well as Iceland, Norway, Monaco, Switzerland and Liechtenstein.
Residency Application as an EEA Citizen
As an EEA citizen, all you need to do is to show up at the local town hall or maison communale to get yourself registered as a resident within eight days after arriving in Belgium.  The document requirements vary from commune to commune, but generally you will need your passport, three passport-sized photographs, as well as proof of means of support whilst living there.  You may also need to show your birth certificate and marriage certificate.
Residency Application for non-EEA Citizens
If you are not a citizen of any EEA country, you will need to submit more documents than the ones listed above.  You will also be required to submit a medical certificate signed by a doctor accredited by the Belgian embassy.  A certificate of good conduct or your criminal history record from the police authorities in your last country of residence may also be in order.
After you have submitted these documents, the Belgian police will visit your Belgian address to verify your residency.  Then you will be given a temporary residency permit for three months.  Your temporary residency can be extended to six months or five years if you produced proof of employment and social security along with your other documents.