8 Guardian Forces
Summons return once again, this time the form of Guardian Forces. They actually play a bigger role in Final Fantasy VIII than they ever have in the past: now, when you summon a Guardian Force, they're not just there for a single turn, they'll fight for you turn after turn as you issue commands.
In many ways, they almost play as a replacement to materia from Final Fantasy VII: not only can they fight for you in battles, but they'll also help to determine which abilities you can use in and off the battle field.
There may seem to be a bit of a learning curve when you first start junctioning, but it's actually quite simple once you get used to it. First, you'll need to junction a Guardian Force to a given character. After the GF is junctioned, you'll be able to junction magic to different stats for the given character. You can either do this manually and take into account the surroundings and possible impacts of your decisions, or just set it for automatic and let your fate rest in the hands of the dice.
When assigning abilities, make sure to give almost every character the Draw command; it'll be quite useful not only for the actual battle, but also to stock up on magic to junction later on. At least one person in your group should be able to use Items and Magic.
Guardian Forces, just like the characters they're attached to, grow. As your characters level up, so will your Guardian Forces. This allows them to learn new abilities, and increases their HP and Attack power.
When a battle's over, you'll receive a screen that shows how much experience and AP you've gained. Experience plays into leveling both the Guardian Forces and your characters. AP is used to teach new abilities to a Guardian Force. You'll only earn AP if a Guardian Force was junctioned to a character in the battle.
Guardian Forces in Final Fantasy VII are almost like pets: they'll grow attached to characters that like them. There are a number of ways to increase the Compatibility of any GF with any character, and they range from using a certain elemental spell to finding and using certain items. However, the easiest and best way is even more simple: if you continue to summon the GF, the compatibility will increase.
The higher the compatibility, the faster the Guardian Force will show up in battle. If you intend on using the Guardian Force at all (especially during boss battles), you should definitely have your compatibility pretty high- 750 or so would be a bare minimum, but the closer to 1,000 you can get, the better.
An item called Amnesia Greens can be found that will allow a Guardian Force to "forget" and ability. At first this may seem pretty odd; why would you want to forget an ability? Actually, this may prove to be very useful: you can forget abilities and replace them with one of your choosing by finding the right items.
Missed a Guardian Force?
If you miss out on drawing a Guardian Force during battle, don't worry: during disc four, you can draw them from the appropriate enemy in Ultimecia's Castle. Siren can be drawn from Tri-Point, Leviathan from Trauma, Pandemona from Red Giant, Carbuncle from Krysta, Cerberus from Gargantua, Alexander from Catoblepas, and Eden from Tiamat.
Secondary Guardian Forces
Odin - Once inside the Centra Ruins, find and defeat Odin. Once you do, he'll join your party. Odin isn't a Guardian Force that you can control: he'll randomly appear during the start of some battles. Odin will appear roughly in one out of every ten (non boss) battles and instantly destroy the enemies on the field by slicing them in half with his Zantetsuken.
Phoenix - Phoenix can be summoned only by using the Phoenix Pinion in battle. Once you've summoned Phoenix, there's a chance he'll show up when your parties in trouble.
Boko the Chocobo - After solving at least one of the Chocobo Forest puzzles, use a Gysahl Green during a battle. Boko the Chocobo will appear and attack the enemies.
MiniMog - By using Mog's Amulet, a GF can learn the MiniMog ability. When he's called upon, MiniMog will appear and dance. This will restore all of your GF's HP. This becomes more and more useful as you go further into the game.
Moomba - Use a Friendship item during a battle and a Moomba will come to your rescue and attack the enemies.
Gilgamesh - During disc three, if you've already gained Odin, Gilgamesh will begin to appear randomly. Like Odin, you won't be able to control him. Gilgamesh, however, isn't just restricted to showing up at the start of a battle, and he can also appear during boss fights. Gilgamesh will use a separate attack based on which of his four weapons he decides to use.