to put it in a different way: Decide upon a way to send data. Most muC have either 8-bit or 16-bit ADCs. If you use an 8 bit adc it can be very easy as a serial port in general works on bytes. So each value that you receive on the the ComPort / serialPort on your PC is one value, that you can take, display and save directly (by using any kind of container, a ring buffer would be a good idea in your case). a 16 bit ADC needs you to combine 2 consecutive bytes. Demands a bit of logic but is essentially the same. Though very simple this is already a protocol. You can also think of a more complicated way to communicate between muC and PC depending on what you want to achive beyond just a few ADC values. You could for example use a char to indicate whether a value was send or a command, or any other information.

Though unlikely you should always consider that your muC can be faster than your program, depending on the speed of your ADC, the things you do in your program and the general load on your Computer.