what do you mean by 'real time'? e.g. how many samples/sec and how many bits /sample?
if a few hundred 8 bit samples/second you could transmit the data over a serial line - it depends on the maximum baud rate you you achieve.
USB could be faster depending on the protocol used and ethernet much faster (but you would probably have to move to a PIC24 or PIC32)
you can transmit byte data as single characters, 16 bit data as two characters, etc.
the C# program receives the data via the com port object and plots it