Okay, Let me make this Really Clear.
Step 1 - You walk into the Safari Zone
Step 2 - You run around in the grass
Step 3 - If you run around long enough, you'll eventually run into a Dratini
Step 4 - Throw Safari Balls at Dratini until you catch it
Repeat process until your Dratini is Caught, he doesn't have a Very High catch rate, or appearance rate, so it might take a little while.