Connecting to a modem is only one of the tasks you'll have to master. Before you start to worry about how to connect to a PLC through a modem, you'll have to figure out how to connect to the PLC directly through your computer's serial port.
For that, you need to identify what type of PLC you want to talk to. The reason we need to know that is because different PLCs use different rules to do serial port communications. These sets of rules are called 'protocols', and each brand of PLC has its favorite protocol. The closest think to a universal serial protocol is one called Modbus RTU, often referred to simply as Modbus, but sometimes identified as RTU. This is the standard for just about all Modicon products, but many brands of PLC can also use it.
Once you decide on your serial port protocol, you'll need to add control for the modem to tell it what telephone number to dial and how to deal with the response it receives from the telephone on the other end of the line. The driver that handles communications with the PLC doesn't care whether the data it sends and receives is coming through a modem.