Author: Orson Scott Card
Publisher: Tor Books, 1986
This is the second book in the Ender's Game series -- kindov. You can just as easily read Ender's Shadow as the second book, and then Shadow of the Hegemon as the third, even though they are technically books 5 and 6. These three are actually sold as a boxed set, and seem to work together better as a trilogy than the Ender's Shadow, Speaker for the Dead, Xenocide trilogy. I would probably recommend reading Speaker for the Dead as book number four, after SotH, or whenever you get tired of the Earth-bound books (I think there are five now).
But anyway... Speaker for the Dead starts out on the Planet Lusitania, where the settlers have discovered that the native 'Piggies' living in the forest are intelligent. These are the first sapient aliens discovered in the three thousand years since Ender the Xenocide killed the Buggers, so it's a big deal. The human settlement is walled off, and the only ones allowed to pass through the gate and interact with the Piggies are Pipo, Libo, and Novinha, the xenodors (xenologers). They are trying to learn as much as they can about the Piggies while staying (mostly) within the exceedingly restrictive rules laid down by the Starways Congress.
Meanwhile, Andrew Wiggins (AKA Ender) is on the nearby (22 light years away) world of Trondheim with his sister Valentine. Although it's been about 3000 years since the end of Ender's Game, they have been planet-hopping constantly, and through the relativistic magic of near-light speed space travel, they are biologically only in their thirties. Ender is still traveling with the Hive Queen, looking for a place for her to settle down and repopulate the Bugger race. He is also accompanied by Jane (first introduced in the short story The Investment Counselor), a monumental AI that controls (in fact is) the ansible network and the all computers tied to it.
When one of the xenologers is murdered by the Piggies, a call is put in for a speaker of the dead. Ender is the closest (Lusitania is catholic, and does not have any speakers of its own), and he sets out on the 22 year long journey to meet the xenologers and the Piggies. In doing so, he finally parts from Valentine, who is married and settled on Trondheim. But he may finally have found a home for the Hive Queen, and be able to Speak for the Piggies (Speakers for the Dead don't have to Speak only for the dead).
That's as far as I can go without giving you spoilers, except to tell you some of the themes of the story -- the planet of Lusitania's very weird biological systems, the familial strife of the Lusitanias, politics with alien species, and fun with other languages, most notably Portuguese (you don't need to understand any Portuguese to enjoy the book, but if you do, it's a bonus).
This is a good book, but don't read it before you read Ender's Game. If you have read Ender's Game, this is a much more developed, in-depth book. It also moves away from the feeling of the first book, without the war, the games, the plotting, and the little kids. If you want more of the same, read Ender's Shadow. But if you want to find out what happened to Ender, this is the book.