Describe some things that happened as the characters tried to solve the problem in Ender's Game?
This sounds like a homework assignment, so I'll just give you some tips to get you started. How you answer the question depends on which character's problems you focus on.
In Ender's Game, the human race is fighting against its own extinction. Earth is threatened by a race of alien creatures called buggers. The adults in the book manipulate Andrew "Ender" Wiggin into commanding the battle against the bugger threat. They realize Ender has the potential to be a military genius, so they take him from his family and send him to a military academy called Battle School in outer space. There, they purposely isolate him from the other students in order to make him work hard to become a leader among them. They present Ender with harder and harder challenges in the form of military games. In the end, they set Ender to work playing a game of command. Although Ender does not know it, he is really commanding an invasion against the bugger worlds.
Ender has a different problem. He knows that the buggers are out there, and that he has to fight them someday, but he never knows he is actually fighting them until after he has defeated them. His main problem in the book is that his teachers keep presenting him with challenges, and these challenges are very dangerous. He struggles against social isolation, bullying, and stress. He has fights with bullies and finds creative ways to win games when the odds are against him.
To do your assignment, you first need to choose whether you want to write about what Ender does, or what the adults do. Then look through the book to find the specifics about those characters' actions. If you feel overwhelmed when you look for major events in the whole book, start by reviewing a summary (link below). You might also want to look at the analyses of the characters. If you focus on Ender, you should read about Andrew Wiggin (link below). If you want to focus on the adults, you should read about Colonel Graff, Major Anderson, and Mazer Rakham (link below).