Getting a "timestamp" of when data is collected is entirely down to you.

Most Arduinos don't have any concept of the current time, only the time since the program started running. To know what the time "now" is you have to have some mechanism to tell the Arduino what the time is, along with a method of keeping track of that time.

There are devices called Real-Time Clock (RTC) modules which keep track of the time for you. They don't magically know the time - you still have to tell them at least once.

You could tell it the time through the serial port to set the clock - from then on (assuming the RTC has power) the RTC will know what the time is.

Another option to get the time into the RTC is to use an internet connection (ESP8266, WiFi shield, Ethernet shield, etc) to perform a Network Time Protocol (NTP) query to a time server on the internet (such as pool.ntp.org) to get the current time and update the RTC. This should be done regularly to correct any drift in the RTC.

Once you have an RTC and a method of setting the time you can query the time whenever you sample some data and store that time along with the data in whatever way is most suitable for your situation.

NTP is the proven way of getting time remotely. NTP libraries, like @Marcel denotes, is making UDP connections to a server with an interval. So you do not need to do any polling to the server before using it.

Here is the usage of an NTP library with a one-hour offset and one minute refresh interval:

#include <NTPClient.h>
#include <ESP8266WiFi.h>
#include <WiFiUdp.h>

#define NTP_OFFSET   60 * 60      // In seconds
#define NTP_INTERVAL 60 * 1000    // In miliseconds
#define NTP_ADDRESS  "europe.pool.ntp.org"

WiFiUDP ntpUDP;
NTPClient timeClient(ntpUDP, NTP_ADDRESS, NTP_OFFSET, NTP_INTERVAL);

void setup(){
  timeClient.begin();
}

void loop() {
  timeClient.update();
}

To get a timestamp or formatted time anytime you want, use the functions:

String formattedTime = timeClient.getFormattedTime();
unsigned long epcohTime =  timeClient.getEpochTime();

You can use this python script as your receiver code. Change 'port' to your Arduino port.

To find your Arduino port, before you plug it in, in the shell terminal use

ls /dev/tty*

Use it again after you have plugged your Arduino in and compare the lists to find the new connection. (For me, it ended up being ACM0)

Do not forget to download serial library if it is missing: https://pypi.python.org/pypi/pyserial

import serial
import time
import datetime

ser = serial.Serial(
    port='COM5',\
    baudrate=9600,\
    parity=serial.PARITY_NONE,\
    stopbits=serial.STOPBITS_ONE,\
    bytesize=serial.EIGHTBITS,\
        timeout=0)

print("connected to: " + ser.portstr)

while True:
    line = ser.readline()
    timestamp = str(time.time())
    #timestamp = str(datetime.datetime.fromtimestamp(time.time()).strftime('%Y-%m-%d %H:%M:%S'))
    with open('output.txt', 'a') as pyfile:
        pyfile.write(line + ' ' + timestamp +'\n')

ser.close()

An accurate enough way is to use the millis() function. It will return the value in milliseconds since the start of the Arduino. If you start the Arduino at a specific time, you will be able to calculate the exact date and time.

Why not an external module?? An RTC such as the DS3231 in merely 5$ and it includes a temperature sensor for you!