Connecting RS485 from PLC to RS232 (9 pin port) on PC (laptop) is simple. But the evolution of computers has made the conversion not quite so simple now days. Most computers (laptops) now days do not have a 9 pin RS232 serial port, but utilize USB ports.
As shown in the video about Allen Bradley PLC Cables (AB PLC cable Demo on youtube), you can not use the AB PIC box (RS485 to RS232 converter cable)with a USB to RS232 converter cable. You must get a single cable designed to convert RS485 to USB. As there are electronics involved, it is not just straight wiring. Then with some PLC vendors, they might slightly modify the protocol so you have to buy the RS485 to USB converter directly from the PLC vendor. Like AB uses what they call "DH485" and sells a 1747-UIC converter to do the job with one cable.
But there may be a work around as pointed out by Brian in reply to this post. You can use a Belkin USB-RS232 converter cable. (The Blue USB to RS232 cable in our video).
When using a USB to RS232 converter cable with the PLC vendor's RS485 to RS232 cable, like the AB PLC cable, you not only have the electronics (needs power from com port), but com 1-4 dependency; but also driver for the USB converter cable, drivers for the RS485 cable and drivers for the PLC software like RSlinks.
All the drivers, software and hardware leave a lot of room for conflicts, incompatibility and headaches. So save your self some headaches and use the 1747-UIC ($300+) or the much less exspensive plccables.com non-oem replacement cable (about $40).