After you meet it at the Burnt Tower, it will go north of Cianwood (As far north on land as you can go)
Then it will go to an island between Ecruteak and Mahogany, past a cut tree.
After that, you find it in Vermillion City, as you're getting off the S.S. Anne, on the way to/from the harbour.
Then it will go to route 14, between Fuchsia and Lavender. It's quite hard to find - start from Fuschia, then when you get to the part where the path is vertical and wide, it's on the water to the right.
Finally, you'll find it where you found Misty (assuming you've already found her - if not, find her). There you'll be able to face it, and hopefully catch it.

Thanks a lot. That really helped.

I have some few questions as well:

-Is it possible for an English TRU Arcus to trigger the special level 1 Dialga/Palkia/Giratina in a Japanese Heartgold/Soulsilver?
-From where do I access the Ruins of Alph?