Those Route billboard thingies will tell you it's raining on that Route by Mistralton. Go there and it should be raining. Walk to that house that's on the way to Twist Mountain and the nice old lady will tell you to come inside her humble abode to escape the heavy rain. Then she'll tell you a lovely story about "The Stormy Pokemon" and that he flies like a genie all over the place and it is your sacred to duty to stop him from causing chaos to the villages, towns, and cities of Unova!
Hold onto your Pokeballs, and here's how ya can catch him!
In case you were asking how to actually CATCH Thundurus, you just need to grab a decently leveled Amoonguss with Spore, and possibly a Pokemon (high levels work best) with False Swipe. So, check the sign where that rascal of a genie is lurking and Fly there PRONTO. Should be thundering and stormy and all that, so just ride around til he shows up. Start out with your False Swiper and SLICE HIM LIKE IT WOULD KILL HIM. After that, he'll flee. Same process, find him but this time use your handy-dandy Amoonguss to Spore him to sleep (this will increase your chances of catching him in the third round [You can use Hypnosis too, but I say Spore/Amoonguss because he's there and it's 100% accurate whereas Hypnosis has that sketchy 70%]). When you find him again, try using a Quick Ball right at the beginning for a better chance.
I caught him in one shot of a Quick Ball, but the results are different for everyone. Keep trying and I'm sure you'll catch him soon enough. Best of luck to you!
