The nineteenth-century civil records for Belgium were microfilmed by The Church of the Latter-Day-Saints, and have since then been digitized. They are freely available at FamilySearch.org. Indexing of the records however is very sparse. You will need to browse the records, so it is helpful to have a general idea of time and place before you start.
In this example, we will look for the birth record of my paternal great-grandfather, Constantinus Smets, who was born in Borgerhout, now part of the city of Antwerp, in 1870.