yeah, the little girl you find in the ruins of the summoners village or what ever it is called, also summons monsters.
The gems is correct. I am sure you start off with one... anyway, equip it as your accessory. you will be able to summon while it is cast, and you gain points every battle which goes towards learning to summon that spell. once you do, swich to a new gem, and learn it. (the only one you just learned can be summoned at any time now).
There is one part of the game, where you are in a forest, and a Eidilon appears, and says you have to find him in the forest 5 times. once you do, you get his gem. he is one of the first you get. can't remember his name... but he does a lightning attack. his name is never the same in any of the games.
hope that helps. (look for something with the name Odin in it. it is not a gem, but will let you summon Odin. Odin rules!)