To accomplish this process, you first need a way to connect the phone's wire to the computer. Older computers had a dedicated port for this job, but the newer ones doesn't . The port from older computers was used to connect the PC to the Internet, when this could only be possible using dial-up connection. To get a fix for this obstacle, I suggest to use Google. There are plenty of easy and cheap solutions for this. Also, there are services provided by firms like Oticon, which gives their users a device that facilitates the connection between the PC and the phone.
After you completed the above step, use the Software Informer's database to find a program that can record, and provide a report for the incoming and outgoing calls. There are plenty of programs with this functionality, so you should be able to do this on your own.