Extort some properties (it will not matter if they want to pay you the money). After that week, look on the map and double click on the property that was extorted. A picture of the owner will appear with details about the shop. Move the cursor next to the picture in the "blank space" and the cursor will change. Click when this happens and the property will become yours. Do not forget to send a man to run the place the following week.

To get easy properties without extortion, use the following steps. Beside the picture are invisible buttons that say (in order) sack hood, return to base, and hood pay. Press the "Return To Base" button and then you own it. Doing this also (one week after the process) allows you to buy the empty area in the middle of tenement blocks.