Final Fantasy VII/Shinra Headquarters

You'll find yourself on the playground, and Barret will be pretty broken up after Sector 7 is destroyed, but he'll be a bit hopeful as he learns that Marlene might be safe. Barret and Tifa will join Cloud, so head toward Aeris' house. You can either grab the yellow Sense materia now or on your way back through to Wall Market. Back at Aeris' house, you find out about the Cetra (Ancients) and who Aeris' mother really was, and Barret will meet up with Marlene.

Back to Wall Market
Barret will suggest that Wall Market might have something that might help you get to the Shin-Ra headquarters, so head there. It's a good chance to stock up with all sorts of stuff. The people will discuss about how the neighboring sector was crushed, the porridge is all ruined, and how all sorts of stuff rained down - and that the weapon shop man grabbed it all. The weapon store man - the one who's constantly fixing up the tank, not the clerk - tells you that you need batteries to get up to the plate. They're not that expensive, so go ahead and buy them.

Stock up on Lightning materia, have at least 3, one for each party member at time. You are heading to a highly technical place next, full of mechanical enemies who are weak against lightning.

The long climb
As you pass Don Corneo's mansion, a bunch of kids will tell you about the cable that just happens to hang down all the way from the World Above and lets you climb the sector wall. After you get up, the place is again fairly straightforward: The yellow sockets need batteries inserted in them, and these let you advance.

There is a frustrating section involving leaping from one side of a gap to the other side by using a swinging bar. Timing is really important. The best way to proceed is to pick some static spot of the background, and hit the button as the bar is at that point, and if you don't make it adjust the spot. The right moment is when the bar is swinging towards Cloud, right before it hits the second prong and pretty close to him, but not quite there.

Entering Shin-Ra HQ
You can save at the front entrance of the Shin-Ra building. Tifa begs you to sneak in. To sneak in, head left and use the side entrance door. You need to climb all the way up to the 59th floor. The only spoils on the long climb are a lone Elixir, and the conversations between Tifa and Barret. You can also do what Barrett suggested and just walk through the front door to the Shin-Ra headquarters. As soon as you head in, you will get attacked. When the battle is over, you can chase the group of people around the lobby, or you can just jump on the elevator at the back of the lobby. However, security alarms start going off, and you'll have to fight random battles on the elevator till you get to the 59th floor. If you get lucky, you'll run into some Shin-Ra employees and they'll just leave you alone.

You have a chance of seeing a Turtle's Paradise poster on the lobby wall, and you will get the another chance to see that when you visit the building at the end of Disc 2 though, so don't worry if you decide to climb the stairs instead. If you really wanted to, you could come back down by taking the elevator at the 60th floor and then go back up after seeing the flyer.