How does the Arduino do serial communication with a PC?
You should look for an FTDI USB to UART IC. You also have prefab PCB's with an FTDI chip embedded. It's really easy: You connect the FTDI with a USB connector to the PC, the PC will install driver. Now you can talk with the PC by sending data over the UART of your arduino and vice versa by using a com terminal program like Putty.

Example: https://learn.sparkfun.com/tutorials/how-to-install-ftdi-drivers/all

You should not worry about conversion and such things. It's really easy. the PC will install the drivers and u just can receive UART data and send UART data to your Arduino. All the conversion is done in the FTDI chip and it's just transparent.