Well for starters I'd suggest training. A lot. Once you have a good team at least to lvl 40 (just to be on the safe side) go to the town you start in and use surf on that route. Follow it to Victory Road. Oh, and the trainers are tough if you don't have a good team ;D
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Right behind the blackthorn gym!
in dragons den you can also catch dratini's in there
I can't say it's easy to get Shiny but Dratini are found in the dragons den behind the last gym.
After you defeat Clair and Lance at the dragons den with your rival,look at your pokegear.If it is anywhere between 6:00-10:00,then go back to the dragons den and you'll see Clair.Talk to her and she will give you her phone number.Then,you can call her back Friday night to arrange a rematch in the Saffron City dojo.
Well there aren't probably any dragons alive today (but they have existed), so there is no such thing as dragon den's anymore. But It's probably a large cave.