Follow the path, using your portals to pass the fence and rubble pile. When you reach the second fence, portal up to the platform behind it, in the upper-left side of your view. From there, drop down from the scaffolding and follow the concrete path. You'll reach a wall which will accept a portal - your destination is a lit platform on a tall tower with '09' painted on it.
From the tower, you can portal over to another high wall on the left side of the fenced off area in front of you. The scaffolding there will lead you to another wall. Portal down to the concrete platform (near the big "Keep Out"), jump down to the other side and continue past the signs. Pull the lever at the end of the pathway to open the door leading to the hatch.
To open the hatch, you'll have to press the override buttons on either side of it in quick succession. Place a portal on the wall next to one of the buttons, and another across the way. Push the button, run through your portal, push the other button, and the hatch will open.
After entering the hatch, move down the metal walkway until you reach a broken door. Portal through the doorway and pull the lever at the end of the hall. Once in the lobby, your goal is to launch yourself through the circle of the giant hanging Aperture logo. Portal up to the metal platform on the top right side of the back wall. Fire a portal onto the angled portion of the support below, then jump through a portal on the ground.
Walk through the sliding door, past a couple rooms, and back outside. Enter the elevator and press the red button to activate it. Once you're at the top, fire a portal onto the angled surface above the vitrified test chamber doors to the left. Walk down the stairs around the elevator to the open shaft, fire a portal at the bottom of the shaft and jump through it to launch yourself to the next door.
Inside Pump Station Alpha, flip the switch in the control room, then walk through the open gate onto the metal walkway. High on the wall to your left is another walkway - portal up to it, then walk down the pipe to the next elevator.
Use the Repulsion Gel to bounce to the other side of the gap. Portal up to the tall platform across from the exit, then jump back into the pit of gel to bounce over to the exit door. Press the button to release a cube. Grab the cube and place it on the big button, then return to the exit door.
Fire a portal on the ceiling above the moving platform, then bounce up to the platform past the Repulsion Gel and fire your other portal onto the wall. Fall onto the moving platform as it passes and retrieve the cube. With the cube, bounce back up to the same platform and portal to the platform across from you to place the cube on the button.
The button will reveal a new surface high on the wall to your right. Shoot a portal onto it, jump through it, and bounce over to the next area, which contains another cube separated from you by a long pit. Jump onto one of the gel-covered side walls to bounce back and forth over to the cube. Retrieve the cube and place it on the button back at the entrance to the hallway.
The button will reveal a second, higher surface on the wall of the main room (to your left as you exit the hallway which contained the second cube). Jump out of a portal on that surface to bounce over to the exit door.
Hop down from the scaffolding, then use the broken bits to cross the swamp. When you reach the main platform, turn to your right - at the top of the tower with the tube protruding from it is a portalable surface. Portal up to the top of the tower, then portal into the test chamber.
Pressing the button in the chamber will release blobs of Repulsion Gel. Press it, then turn around and run to the far wall. On your left will be an elevated platform - portal up to it, then place a portal beneath the blobs, and one on the wall next to you, to cover the platform with gel. Use the gel to bounce up to the next level.
Now cover the floor below you with Repulsion Gel in the same manner, so that you can bounce up to the platform across from you. Hop across, then repeat the trick to bounce up through the Emancipation Grill. Fire a portal onto the angled platform, keeping your other portal beneath the falling globs. A glob of Repulsion Gel will exit the portal on the platform and fly to the edge of the gap between you and the exit. Now launch yourself out of that same portal by falling through the floor, and you'll bounce off the gel and over the gap.
There's a button set into the far wall. Use your portals to splatter a blob of Repulsion Gel beneath it. Now move your portals so that the gel is flying out of the wall behind the metal grate. Jump up and hit the button, which will turn off the water. When a glob of gel hits the bit of floor the water was hitting, use it to jump up to the next area before the water turns on again.
In the second section, launch some gel out of the angled platform, so that it splatters on the wall. Portal up to the scaffolding high on one of the walls, and jump through a portal on the floor and through the angled platform to fly into the gel on the wall, which will bounce you out to the third area.
This bit's a little tricky if you don't know where to look. Walk up the stairs and to the edge of the metal platform (into the box with the portal surface). From there, you'll see a large open area with a couple of concrete towers. The tower on the far left has a lit portal surface near its top - fire a portal onto it, turn around, and walk across a short metal walkway until you can see into the test chamber where Repulsion Gel is dripping. Shoot a portal beneath the gel.
The gel will splatter onto the angled surface of another tower. Now fire a portal onto the ground below the metal box and launch yourself into the gel, which will bounce you up to Chamber 28. Walk around the scaffolding and portal up to the next level (it doesn't really look like you can, but you can).
Fire a portal above the cube, and another beneath the dripping Repulsion Gel. The cube will bounce around until it breaks out of the glass container - catch it and wash it off with the water. Put the cube on the button, which will lower an elevator. Use a bit of Repulsion Gel to jump up to the elevator, then recoat the cube with gel to bounce it off of the button, raising the elevator.
After exiting the elevator, you don't need to go far into the Aperture building except for the sake of exploration. After you walk a little ways down the hall, turn around and you'll see a portal surface next to the entrance. Fire a portal onto it, then walk back outside (toward the elevator you came from) and fire another portal onto the wall with "1971" painted on it.
After entering the door, fire a portal onto the bottom of the far wall, and another above it to access the high scaffolding. There are two portal surfaces on the floor below you - fire a portal onto each one, and jump through the one nearest to you. After you fly out of the far portal, you'll see a portal surface high on the wall across from you. Fire a portal onto it (keeping the one below you, of course) to launch yourself out of it and into the Pump Station control room.
Pull both Gel Pressure levers and exit. The next area contains the main control room. To get there, portal up to the scaffolding on the wall next to it. Standing on the edge, with the Control Room to your left, you can fire a portal into an angled surface on your right, and another below you to launch over to the Control Room entrance. There you'll find GLaDOS being accosted by a bird - walk into the glass-walled room to scare the bird away and pick up GLaDOS. (For an Achievement/Trophy, find a door in the Control Room which is half-covered by a file cabinet and explore.)
Return to the platform you used to access the Control Room. This time, you're going forward, to the walkway which was raised in front of the elevator. Fire a portal high on the wall behind you, then jump through another on the ground.