Summons have once again returned in Crisis Core. These great beasts are activated through the DMW randomly. The first three summons are fought through the story line. But you will have to find their respective Materia through the missions. The Odin Materia is also acquired through the missions, but you are not put to a fight with him. The Phoenix Materia is not obtained until later in the game, when you go to Nibelheim. You must complete the first of the "Seven Wonders" sidequest. Below is a brief detail of each summon, their CGI, and where they are located. It would be greatly beneficial to get them as early as you possibly can.
Complete mission 8-1-1
Hellfire Ifrit brings about a world of fire, and throughs it to your enemies. This attack will ignore enemy SPR.
Complete mission 8-1-4
Mega Flare Bahamut launches a ball of energy at the enemies. This attack will ignore enemy SPR.
Complete mission 8-5-6
Exaflare Bahamut Fury uses the moon to create a super-charged energy attack, and launches it towards the enemies. This attack will ignore enemy SPR.
Complete mission 8-1-6
Zantetsuken Odin races towards te enemies, cutting them down with his blade. This attack may not always connect.
1st Wonder of Nibelheim
Rebirth Flame Phoenix rises to the heavens, and incinerates the enemies below, in a firey blaze. This attack ignores SPR. This will also give Zack the Raise status.