What are the title and author of the young-adult book about children
playing video games to train to fight aliens, but in the end the main
character finds out he was actually fighting the real aliens?

Hello.

It sounds like you're describing "Ender's Game" (1977) by Orson Scott Card.

From a review of the book:

" The young genius is taken from his family when he's only six and
placed in an off-planet training facility called Battle School, where
he and other prospective warriors are taught to fight...
Then the day comes when Ender, having played a simulation in which he
destroys the bugger homeworld, learns that all those simulations were
actually remote-controlled real battles. He's actually been leading
the Earth fleet in an invasion. And he's just blown up a planet."
http://www.aml-online.org/reviews/b/B199765.html

The book is available from Amazon.com:
http://www.amazon.com/exec/obidos/ASIN/0812550706/

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search strategy:
"game turns out to be real"

"Ender's Game" matches your description and I hope it's the book that
you had in mind.  If not, please let me know via the "request
clarification" feature. Thanks.

Perfect.