You'll awaken in Junon. Barret will be the leader, but there isn't much you can do. You'll find out that you're all to be executed in a televised event.However, just as the gas in Tifa's chamber is turned on, Emrald Weapon attacks Junon, and you're given a chance to escape.You'll try to open the door, but without success. You can't open it, so don't worry about it. Just hurry and get to the landing pad. (If you've already gotten Yuffie, she'll be disguised as a TV reporter. Talk to her, and she'll join with you. All you have to do is make it to the Highwind. After that, they can take care of themselves. Meanwhile,you have to save Tifa from her plight. Don't worry, she can't die, no matter how long this takes you. Just do it in this order. First, hold down the button so that she can get the key with her foot, then move her head and feet at the same time. Now move her head and left arm at the same time, then both arms. You should be able to figure it out with only minor difficulty. Then use the button to the left of the chair to turn off the gas, then make your getaway! You'll run into a snag only when you reach the end of the line, when Scarlet will catch up with you. If you want to win the little slapfight (you don't get anything for it), hit 0 the button as soon as Scarlet raises her arm. The airship should appear just in time to make your escape, and you'll be free.
Now that you have the airship, the rest of the world is pretty much open to you. (Except the underwater parts, but I'll get to that later.) If you play the song on Tifa's piano again in Nibelheim, you'll get another Elemental materia. Also, by now you'll be strong enough to tackle the Midgar Zolem. You might want go and fight him, because that's the only way to get the Enemy Skill Beta. Toget the spell, try using Bio 1 on him, then just waiting. Be careful not to kill him before he casts it though. The shops in Costa de Sol and Junon are selling better stuff now, and so are the shops in Rocket Town. Rocket Town also now holds the Fourth (yes, I know this is supposed to say Force--the translators slipped up here) Bracelet and a Guard Source in chests scattered around the town. You can get the Full Cure materia in the back of the item shop in Cosmo Canyon now, and you can also start raising Chocobos if you care to do so. The chocobo ranchers have lots of information on the subject, as does the rather forgetful Chocobo Sage in the Icicle Area. To find him, fly around in the Highwind until you see a little secluded house in the mountains. The green chocobo there will give you yet another Enemy Skills materia if you talk to him. If you constantly return to the Sage's house throughout your adventure, he will eventually give you the full instructions for raising a Gold Chocobo. It takes him literally FOREVER to remember the whole process though, so I finally just asked one of my friends. He explained the whole process in 5 minutes, so I would just ignore the Sage (Except for buying Sylkris Greens). Finally, you now have access to two uncharted isles, Cactus Island (in the lower left-hand corner of the map) and Goblin Island (east of Icicle Area). Cactus Island has some of those annoying little Cactrot enemies just like the ones from FF3, except these are called Cacteurs. The only interesting thing about them is that you can morph them into a Tetra Elemental, a very good acssesory which absorbs damage from fire, lightning, ice, and earth magic. Cactuers are very hard to hit, and have 6,000 HP, so to Morph one, I suggest following these steps: Manipulate one, then use it's 1,000 Needle attack 5 times. Then just morph it using one of those 255 accuracy weapons like Tifa's God's Hand. (Use this one instead of the Sniper C-R, becuase God's Hand has a higher damage rate.)
Goblin Island is only slightly more interesting. In the forested areas, you will meet up with Goblins, which are the only creatures in the game to posses Zeio Nuts. Zeio Nuts are essential in getting a Gold chocobo, so you should come here at least once in your travels. They also possess the Enemy Skill "Goblin Punch", a basically worthless attack that will only hurt an enemy if the caster and the target have the same level. Since this will almost never happen, Goblin Punch really has no value. (Except if you're trying to collect all the Enemy Skills.)
When you're done doing what you want with the Highwind, you'll have to eventually head south to Mideel.