First, a disclaimer. Don’t buy property until you have lived here for at least six months and a year is better.
That said, the process is not particularly unusual if you have done this in the U.S. Normally the transaction involves a lawyer representing the seller and another representing the buyer. They buyer’s lawyer needs to do his homework to make sure the title of the property is clear and that the property description actually matches what is registered.
Generally you end up with a title document recorded with the municipality. One exception is in the case of waterfront (lake or ocean) property where you are being granted a lease. Don’t panic here but make sure your lawyer knows what he is doing.