The summons that you do not automatically receive due to storyline are listed below:

Walk behind waterfall centered behind Worus Castle.
Go back to Pirate's Cave. Syldra's Spirit emerges from water in a scenario which Faris sees Syldra
Go to Jacole cave. Go through the whole cave until you reach the basement of the castle of Bal (Galuf's Castle)
Search Istory Falls with your submarine. Find the tunnel which you can go to a different part of the world map. Emerge. Walk around the forest until you encounter Shoat.
Catch a Black Chocobo, at the town of Mirage. Fly to the desert where North Mountain is. In the SW area of the desert is Pheonix Tower. Land. Go in it.
Go to North Mountain, after you have the 1st tablet. Bahamut is at the top of the mountain

The Final Spells:
Enter the town of Mirage, and go to the magic shop. Have the passages ability on, and you can see the hidden passages in the shop. Walk until you find the hidden room with a merchant. The vendor will sell you the last set of magic spells.

The town of Mirage is located on the southern part of the world map, towards the east a bit, on the narrow line shaped land connector between the south eastern most continent, and the south western continent. This long narrow strip of land spans across almost the entire world map. On this land strip/connector, is a tiny cluster of trees. These trees are the type you can land your black chocobo into. You enter this tiny cluster of trees on foot. There, you're in Mirage. Refer to the world map within the game, if my scew description is throwing you off.

Level with ease:
- The desert: near North Mountain and Phoenix Tower are, have the best AP, EXP, and Gold after battle.
- Phoenix Tower: Magic Pots (which require Elixers to kill, & there are very few in the game)
- Cleft of Demiension: Monsters are hardest here, out of the whole game.

- Have the Passages & Dash (theif abilities) learned and equipped throughout the game. This gives you a greater advantage.
- Stuck? Check all the towns you can go to in the world, and you will eventually find out what you need to do to continue the game.
- Having Gogo problems? Don't attack. (He won't if you won't :)
- Stuck in a dungeon, and want out? Use the Time wizard's Exit spell. (spell found in world 2)
- 2 hidden swords in the town of Mwa. The Brave Sword & the Chicken Dagger. It is possible to get only one of the 2. The Brave Sword has very high attack power, and decreases if you run. The Chicken Dagger has very low attack power, and increases if you keep running (but don't escape battle).
- Play all of the pianos in every world, and the bard at Cresent Island will give you "Hero Song" in world 3. It increases your levels during battle.
- Learn the X-fight ability (Archer) & 2-hands ability (Ninja). Be a Ninja and use X-fight. This allows you to attack 4 times with each weapon you have.