Instructions
Travel to Fuschia City. Fuschia City is located to the south of both Celadon City and Lavender Town.
Head north and enter the Safari Zone. The Safari Zone is a special Pokemon preserve located in Fuschia City. It is home to many Pokemon that can not be caught anywhere else.
Walk around the Safari Zone entrance (Zone 1) until you encounter Tangela. Tangela can also be encountered in Zone 3, which is accessed by going north from the entrance to Zone 2 and then heading west. Tangela is a rare find in either of these zones, so prepare to do a lot of walking.
Throw a "Safari Ball" at Tangela to catch it. You can not battle Pokemon in the Safari Zone. Instead, you must either throw rocks or bait at them. Rocks weaken Pokemon, but they also make them more likely to run away. Bait keeps Pokemon from running, but makes them harder to capture.