The first thing that you should do once you enter the Giza Plains is travel directly south (straight ahead) until you reach the Nomad Village.
Speak to an NPC (non-playable character) on the west side of the village named Masyua. She will ask if you have come to see the Dark Crystals. She will then give you some information about how to obtain a Sunstone and will tell you that you must seek out one of the children nearby named Jinn. Lastly, she will ask for your assistance to help track down Jinn as he wandered off into the plains.
A short cutscene will take place after the conversation with Masyua and Vaan will run into Penelo. Penelo will offer to join Vaan as his first party member as he explores the Giza Plains in search of Jinn.
Penelo starts off with some License Points which you can spend on Licenses as you see fit. It is a good idea to have Penelo start learning some of the spells that are now available, including 
Fire, Thunder, Blizzard and some of the debuff spells located to the right of the White Magick 1 License that she starts off with.
Have her learn Blind, 
Slow and 
Protect as soon as possible. Note though that in the Zodiac Age version of the game you will have to select a job (and eventually a backup job) for Penelo. Check out the Jobs Section for more information.
Penelo also comes pre-equipped with some Gambits already in effect. You cannot view these Gambits yet (until later on in the game when you receive an explanation about how Gambits work) but you can turn them off by pressing the 
Button on the world map, scrolling left or right to reach Penelo and toggling Gambits either on or off. Her default Gambits will have her attack the same target as the party leader (Vaan) at all times, so you may as well leave them on.
Lastly, she gives Vaan a few items before they leave the Nomad Village, specifically: 3 
Potions and 2 
Phoenix Downs.
In the Zodiac Age version of the game, the Black Magick 2 spell Blind can be found in the Giza Plains in the Toam Hills area. Make sure that you find it before you leave this area as this negative affect status Magick will come in extremely useful during some of the more difficult fights of the game. Use the map below to help you find it by looking for marker (1).
Now that Penelo has joined Vaan’s party, a couple of the Hunts become more easy to complete, specifically:
The next Hunt, listed below, is a little bit more difficult and requires some preparation. Level up your characters to level 5 or 6 by traveling to the Dalmasca Estersand (Sand-Swept Naze) which is located just north of where the Flowering Cactoid can be found.
Battle the enemies in the area until you reach a high enough level. You can also travel to the Nalbina Fortress to purchase some more advanced Magicks, Technicks, Weapons and Items before initiating the fight.
Completing Hunt 03: Dalmasca’s Desert Bloom allows you to begin the Desert Patient side quest.
In The Zodiac Age version of the game you can already purchase 
Decoy from the Clan Provisioner in the Muthru Bazaar in Rabanastre. This is an incredibly useful spell that can help you start to form a proper party with a tank. Check out the Party Setup page for details.
With Hunt 02: Wolf in the Waste and Hunt 03: Dalmasca’s Desert Bloom taken care of and the Desert Patient side quest initiated, you can now get back to the main game and begin tracking down Jinn.
The missing child can be found directly south of the Nomad Village at the southernmost end of the Giza Plains in an area called the Crystal Glade. When checking the map, the area can be easily identified as the area with the second Save Crystal at the bottom of the screen. Use the map and the screenshot below to help you find it and travel to that area speak with him.
Jinn, the Nomad Youth, will explain that he was injured while running from some monsters. He asks for your help in creating a Sunstone. Choose to “explain the situation” to him and he will give you a Shadestone.
He explains that, in order to turn the Shadestone into a Sunstone, you must seek out the Dark Crystals all over the Giza Plains.
The Dark Crystals are the large glowing rocks that Jinn points out – they are also pointed out by the game on the map of the Giza plains and are located in each of the four corners of the plains. Travel to all four of them and choose to “hold the Shadestone up to the crystal” until the energy level reaches 100%.
You may not need to reach all four Crystals in order to complete the quest and you will automatically return to the area where Jinn was found once the Sunstone is fully charged.
Jinn will confirm that the Sunstone is complete and ready to go and will ‘race’ the team back to the Nomad Village. The story continues automatically and returns Vaan and Penelo to the village. Masyua will thank you for your troubles and reward you with 50 gil, two Potions and 2 
Teleport Stones.
You are done with the Giza Plains for now. Travel back to Rabanastre and take the Sunstone to Old Dalan in Lowtown to move on to the next part of the story. Old Dalan will give Vaan the Crescent Stone which will give him access to Storehouse 5 and the Garamsythe Waterway.
(Click on the map to enlarge)
