There are 2 ways to train up your skill to GM.
Raising by taming, which is explained by the wiki:
http://uoex.net/wiki/Skill_Guides#Animal_Taming
or
raising by creating pet dyes.
(which was also explained in the 2nd link)
0 - 30, Buy the skill from NPC
30 - 40, create normal pet dyes
Buy taming jewelry with a total amount of +20 to cover the break to 60 taming
or
tame animals until you reached 60 taming.
( 40.0 - 41.1, Black Bear, Llama, Walrus, Polar Bear)
( 41.1 - 47.1, Brown Bear, Cougar)
( 47.1 - 53.1, Alligator)
( 53.1 - 59.1, Panther, Grey Wolf, Snow Leopard)
( 59.1 - 60.0, Snake, Grizzly Bear, Great Hart)
60 - 80, create unique pet dyes
(If you used taming jewelry and reached 80skill, wear them off.
Real skill will be now 60, so you can start creating dyes again.)
80 - 100, create rare pet dyes
To go over 100, you need a power scroll.
The following is to explain, how to reach 120 taming:
(As far I know, there is no way to do that by taming animals)
Macro animal lore to 100!
(my guess, there is no need for any detailed info, how to do that, aye?

)
Wear taming jewels with +15 to be able to start pet leashes.
when hitting 120 (means you have 105 real skill), switch the jewels to just +10
start again creating pet leashes.
When hitting 120 again, switch the jewels to +5 and start again.
When hitting the last time 120, wear off all taming jewels,
you got 115 real skill now and start the final round until you reach 120.
IMHO, there is no need for using a skill ball.
There are some more time consumpting skills, where a skillball has better use.
I hope, this was detailed enough.