The easiest way is to just buy it at the game corner. That's what I did to get my Dragonite. They end up at level 15 with pretty good stats. Something that might catch your attention is that it know Dragon Rage, which takes down 40 HP no matter what. It costs 2,100 coins in the game corner. Or you could go to the Dragon Den which yields Pokemon at around levels 15-20, but I do not know how to catch a Dratini there.
Improved by Un1ted4rmy:
The best (and easiest) way to get a decent Dratini is by using the good rod (which you get in Kanto) and fish in the Dragon Den. If you have the good rod, then you automatically get a lvl 40 Dratini. Once you level it up once, you will get Dragonair. Then, at level 55, it will evolve to Dragonite.
Hope this helps.
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It evolves at level 30 in dragonair and again at level 55 in to dragonite
You just gotta act like Ash (with his "I love Pokemon!" Attitude).
There is no easy capture just luck but for the beginning its easy to catch some pokemon.
Yes because i have one and it knows surf