I made it to the Giant Chasm but I have no idea on how to reach Kyurem because the trees are in the way in that plain area inside the cave. Is there another way to get to Kyurem?
Just continue foward along the path. You kind of spiral towards the center. Eventually, you'll come to a point where you hear a roar, followed by a Blizzard. The entire area will become covered with snow, and you'll easily be able to reach the cave.
You have to try and get to the lake in the very middle of the forest, and you will hear a roar like Trachy said, then the whole forest will flash freeze. When that happens, go straight forward and into that cave and be ready to battle. He's a tough one, took me over 20 dusk balls. Good luck! ;)
After you come out of the cave, just follow the path until you reach the pond in the very middle of Giant Chasm. Then you will hear a roar and the whole place will turn white. When it clears, you will be standing on a LOT of snow. Find the staircase in the upper right corner of Giant Chasm and go into the cave at the top. Kyurem will be waiting and you will go into battle.
Good luck catching him! =)