Call arriving or relatives in the city where he lives and find out they have a number of flight and time of departure.
If this is not possible, find out which airport the plane coming from the city of departure of the traveler. If the airport in your city only one, just find out in reference in how the plane flies and what a flight.
But if your relative arrives, for example, in Moscow, the case is much more complicated. In Moscow, five state-owned airports and is also private. However, the latter can not take - they have a completely different service system. But in other airports you have to call for a long time (the line usually loaded) to determine the time of arrival of the aircraft from the desired city and number of flight. Well, if the day's flying only one aircraft, but if there are several? In the different airports? Moreover, it is important to take into account the weather factor, which can delay a flight or cancel it altogether. In this case, will have to try to do them all.
Not to sit on the phone, you can use the Internet. In Yandex there is a service called "Schedule" http://rasp.yandex.ru/map/air/#center=60.315781%2C61.106265 zoom=6. To the left you will find search boxes. Knowing only the city of departure, you can obtain information on where and when your relative arrives. Enter the name of the point of departure and point of arrival, and the system will select all the possible options.
And, by the way, today, every major airport has its own page on the Internet with electronic schedules. After spending some time at the computer, you will have full information on arrival and roome of flight of the aircraft.