Before you all go naming your griffins "Buckbeak" lemme lay some mythology on ya. Buckbeak from Harry Potter was actually a hippogriff which is a horse combined with a eagle. A griffin is a lion combined with an eagle. Just keep this in mind before going on a Buckbeak naming spree.
How to tame a griffin. Step 1: prepare. Step 2: find griffin. Step 3: build trap and lure griffin. Step 4: lure griffin but it gets out even tho THE GATES ARE NEXT TO EACH OTHER WITH NO GAPS. Step 5: build new trap. Step 6: gather a load of prime meat. Step 7: lure griffin and knock it out. Step 8: feed griffin prime meat but it All spoiled. Step 9: go get more prime. Step 10: finally feed it the prime and narcotics. Step 11: wait 18373638283737 year's. and step 12: take it out for a spin but get killed by two lvl 300 Alpha Rex because you had it on passive. Step 13: DO IT ALL OVER AGAIN CUZ YOU CANT BE HAPPY WITH A WYVERN OR ARGENT.