After beating the game (I'm not sure if you have to beat it both times for Kyurem to be available or not) head to Giant Chasm (I can give you a guide there if you want) It looks very simple at first, but many challenges await you. First you must enter the cavern in the middle of the entrance. Once inside you will be in a dark room. You may collect items if you wish (as there are a couple of rare items in the whole of the chasm), but the main goal is to reach Kyurem. Firstly you need to go all the way around the cavern and reach the exit (HM Surf is required at this point so make sure you have a Pokemon who can use this as I found out when first doing this myself!). Once you exit, you will return outside.
You will be introduced to an extremely large and complex maze for you to go through. The objective is to get to the middle where a pond-like area of water lies. This looks impossible at first, but there is a way. To do this, the easiest way (without wanting to collect items) is to go as far North as you can from the entrance, then as far West, then as far South, then as far East, then as far North again (make sure you do not go over a ledge which takes you to a part where you have already been, as this mucks up the order). Then go through a patch of long grass and you will see the pond like area. Go to it and you will hear an Earthquake-like roar.
After this sound, the ground will cover with snow (the roar was Kyurem and the snow was his doing in case you hadn't realized . This now gives you an clear passage to the exit and the final cavern in which Kyurem is inside. Walk through to the exit.
Once inside the cavern, getting to Kyurem is a doddle. Simply walk up to him and interact with him. As all legendaries do, it will roar, and the battle will begin.