To take benefit of these prices you will need to prove you are a leisure traveller, en route to the airport, so you will need to provide either your flight details or your holiday booking reference. I don't think you will need to give this when you arrive at the station but you may be asked to provide them on your journey from the station to stansted airport.
Going to the airport by train is great, you can sleep, read a book (even at night), play travel scrabble, or just stare out of the window... The other caveat to buying these inexpensive train tickets from forest-hill station to stansted airport is that there must be at least two adults travelling together. But another great benefit is that children go free. All children under 5 go free, and then one child over 5 but under sixteen per grown up travelling by train to stansted airport.
make sure you leave enough time to get to stansted airport early enough to eat, shop etc, so check the times of trains from the station before you go. If you end up with time to kill at the airport you can always read a book or play travel scrabble again! As you have bought yr train ticket in advance, you don't need to worry about the opening hours of the station.
Or maybe you meant