For the summoner:
First of all, it's only found in the Veira race. You need 2 A-Abilites from both a White Mage and an Elementalist. In order to get an Elementalist, you need 1 A-Ability from both a White Mage and a Fencer.

Monster Capturing:
You need the Hunter class, which is a Human specific class. In order to get the Hunter, you need to master 2 A-Abilites of the Archer class.

In order to capture a monster, you must lower it's HP to a critical state, otherwise the percentage of a succesful capture is next to nil. Putting it to sleep, stopping it, and so on help you, though it does not effect the percentage of capture.

Once you capture a monster, you wil notice that you wil recieve an item, called XXXX's Soul. Morphers are the job-class that are capable of using these items.

The Morpher is a Nu Mou specific class, and can be had by mastering 5 A-Ability of the Beastmaster.

Once you have a morpher, equip the Morpher with the Soul item, and he will be able to learn and use the abilities that come with the Soul. In this fashion, you are able to use abilites that only monsters have.

EDIT: If you have any questions or need further explaining, I will gladly comply.