Presently, the adoption of Internet of Things (IoT)-related technologies in the Smart Farming domain is rapidly emerging. The ultimate goal is to collect, monitor, and effectively employ relevant data for agricultural processes, with the purpose of achieving an optimized and more environmentally sustainable agriculture. In this paper, a low-cost, modular, and Long-Range Wide-Area Network (LoRaWAN)-based IoT platform, denoted as "LoRaWAN-based Smart Farming Modular IoT Architecture" (LoRaFarM), and aimed at improving the management of generic farms in a highly customizable way, is presented. The platform, built around a core middleware, is easily extensible with low-level modules (feeding the middleware with data coming from the sensors deployed in the farm) or high-level modules (providing advanced functionalities to the farmer). The proposed platform has been evaluated in a real farm in Italy, collecting environmental data (air/soil temperature and humidity) related to the growth of farm products (namely grapes and greenhouse vegetables) over a period of three months. A web-based visualization tool for the collected data is also presented, to validate the LoRaFarM architecture.