Ask the traveler which flight he is taking and which cities he is traveling to. You need know the airline and flight numbers as well.
Call the airline and listen to the flight times. If there are delays, the message will include this information so you can be aware when the person will be arriving.
Visit the airline's website. Here you will be able to look up travel information by flights and city. Websites are constantly updated with the most current information. Some websites also have a flight tracker you can use. This search engine allows you to see where a flight is and when it will arrive.