Making the Connection to the PC
From The RadioReference Wiki
We can use receiver control software that will allow you to do several useful tasks; use frequency lists, capture text and images, or even run a Software Defined Radio (SDR) to name a few. However the newer PCs lack serial ports, so we must use a USB-serial connection. This varies greatly by manufacturer, and it's unfortunately beyond the scope of this document to cover them all. However, you're not without resources; most every receiver has at least one associated mailing list somewhere - these are some of the best places to find information on the various requirements each receiver will present to the user. We have a list of such mailing list (though not necessarily complete) in the HF Receiver Mailing Lists article. For mailing lists devoted to certain SDRs, see the SDRs with HF Coverage article.
You may also want to check out the Connecting scanners via USB article, as much of what is written there is also applicable (with a little work) to desktop receivers. Start from section 4 - Generic USB to RS232 Serial Converters. If you are using Win 8 or later, see section 5.3 - Windows 8 Issues and Solutions.
Now that we have the USB-serial connection addressed, what about the audio? A USB/serial connection is not designed to handle audio transfer. This topic is covered in the Connecting Radios to Soundcards article. Click on the link to proceed to this topic.
Receiver, Transceiver and SDR Applications