How to log data to a file from arduino

Using Arduino Programming Questions
5

Are you using the standard Arduino IDE? If not, desist from whatever you are using and install the proper Arduino IDE immediately.
Therein, under Examples, you will find a raft of examples, one of which, in the SD section, is a datalogger writing to (surprise!) the SD card.

Since you don't have an SD facility, you might get some value from trying option 1. I described above.

Here is the code

void loop() {
  delay((1000);
  Serial.print("hello, world!       ");
  Serial.println(millis()/1000);
}

Yes, that's it. Good luck, I'm not in a position to test it at the moment, but sure it will work