Probably illegal but in fedora linux at 9600 baud for standard ascii characters:
tail -f /dev/ttyUSB0 > myfile
to append
tail -f /dev/ttyUSB0 >> myfile
To watch it in another terminal do
tail -f myfile
If they're not standard covert them to decimal or something. You can even output data to a cvs format if you're a bit creative.