how do you tame a monster?
by having smex with it ^^
You have to buy the appropriate item to tame from the Cash Shop. Afterwards, you go hunting for the type of animal that corresponds with the item, except there has to be "Tamable" before the name.
1. You buy a Canine Taming Item.
2. Go to the suburbs of some city and look for a wolf with the word "Tamable" in it's name.
3. You use the item on it.