The possession skill is a class skill that is gained from being an Invoker or Necromancer. It is however possible to possess monsters and minions without having natural skill in the possession skill.
There are three ways you can accomplish this.
Possession Spells
A few classes may get special spells that allow them to possess specific races such as:
Visit the Library > Spells screen in game for more information on Beastmastery spells.
Visit the Library > Spells screen in game for more information on Wildlife spells.
**Possession Items
**It is possible to acquire possession skill through items, although you have to gain a pretty comprehensive selection of possession items as you will need the equivalent skill from items that it takes to possess your pet which for a level 1000 pet would mean items that give a total of 5000 or more possession skill.
Bought Extras
Last but by no means least are bought extras, currently there is a bought extra called the Skull of Corruption it is buyable via the File > Buy Extras > Amazing Items screen for the reasonable price of 5USD.
To possess something you must equip the bought extra then use the Inventory > Spells screen to cast the special spell that is in effect on the item, the item has unlimited charges and you are not bound by restrictive skill requirements so you should be able to possess any level of monster.