On your way inside, you'll be jumped by 2 MPs. When you approach the others, you'll be able to name Cloud and Barret. After the conversation, proceed through the first room to the first bridge. Go up and you'll meet up with Barret and the others at which point Barret will join you. Talk to Biggs to have him open the doors. Talk to Jesse to open the next set of doors. Head to the right before talking to Jesse again to pick up a Phoenix Down. After having Jesse open the last door, press the elevator button to descend.
Go down the stairs and enter the doorway at the bottom. Talk to Jesse to learn how to climb ladders and then pick up a Potion just in front of her. Climb down to where you'll find the first Save Point of the game. Continue to the heart of the reactor and pick up the Restore. Just after setting the bomb, you'll engage in your first boss fight: Guard Scorpion.
As soon as you defeat it, the clock starts. You have 10 minutes to escape the reactor before it blows and the clock does not stop during battles. Return the way you came in, making sure to rescue Jesse or you won't be able to unlock the security doors at the top.