This level introduces a new enemy and new allies that will feature prominently in the coming levels. It does not advance the plot much, if at all, but does have you crawling through much of Black Mesa's extensive ventilation system to get from one area to the next.
After you go down the hallway a bit, you'll come to a leaking steam vent. The door on the left is locked, so just time your passage right to get through the steam without damage. Crouch under the pipes to continue to a room with a headcrab and two vortigaunts. After killing them, grab the shotgun ammo and smash the crates at the far end of the room for two batteries. The door to the right is locked, so climb up the convenient stairs the pipes in the corner provide to access a vent shaft.
There are two grates at the bottom of the shaft. Skip the first one for now and go down to the end and enter the second one, where a medkit and machine gun ammo await you. Go through the door to find yourself where you started and go back up the pipe stairs and enter the first grate. You'll fall through to a room of pipes with another shaft at the bottom.
Turn on your night goggles for this next part. When the shaft widens, you'll find yourself in another room. One tile is already broken, and a sparking wire dangles into it. Many of the tiles will break if you step on them, plunging you into a flooded room of electrified water. Luckily, you can tell the tiles apart by the mildew-esque patterns the damaged ones sport. If you do happen to find yourself in the water, you might as well stop by a table off to the side for a battery, and further up, a health station. After that, climb back up on a fallen shaft and continue on your way.
Fans, Fans, and More Fans
You can hear the fans as you come down the hallway into this next area. Climb onto the metal supports above the two fans in this room and jump across them until you're on the other side. Turn right and wait for the first steam vent to pause before jumping over the railing to the other side to avoid the second one (or, if you're lazy like me, you can run through at the cost of one or two health).
If you're a good jumper, leap across the broken catwalk to the door for some magnum rounds and a RPG rocket (and a zombie). Otherwise, continue to the next fan room on your left. Here you'll have to walk in between the two fans to get to the other side. Climb down the ladder and note that the fan on the right is missing three of its four blades. Time it right and crouch down to enter the vent below it.
After the loading screen, you'll be in yet another vent. Crawl your way out into what may have been a furnace room at some point. Or a crematorium. Regardless, there's fire, and you're probably not going to want to touch it. Jump over the first gap during a pause in the flames, and climb up onto the crates to safely get over the second gap. To your right, there will be a brawny, muscular zombie who will take pleasure in throwing red balls of goo at you. Kill him with the weapon of your choice and watch out for the headcrab as you head to yet another vent on your left. (In case you couldn't tell, vent shaft systems are Black Mesa's most efficient means of travel.)
At the end of this vent is yet another fire room. Crouch to break the gate and walk through the first flame while it's paused. The second flame you don't necessarily have to cross - you'll be going through the hole to your left and out the other end. Be sure to move fast or else you'll become marine barbecue.
As soon as you come out of the tunnel, you'll find yourself ambushed by two goo-throwing zombies. Take 'em out with your shotgun, along with the two normal ones that follow. To your left will be many explosive crates. One of these things is not like the other... push the grey crate (the one that says "DANGER: EXPLOSIVES") into the path of the fire blaster, run up, push the button, and then run like hell away from there to safely watch the explosion that ensues.
Drop down through the new hole in the floor only to be greeted by another goo-zombie and a handful of headcrabs. Keep going and enter another vent.
At the end of the vent is a large cavern of a room. Go straight to drop down to a lower level; in the grate behind you you'll find a couple grenades and shotgun ammo. Drop down to the ground and run over to a dying marine, who warns you to get out of here. It's not like we're not trying, buddy. Raid his truck for supplies and continue forward.
Look up as you enter Storage Room 2 to see a group of new aliens run overhead. To your left will be a button that opens the red doors, but first go to the right to encounter two of those aliens you just saw - pit drones. They'll spit acid at you, similar to bullsquids, or attack you in a zombie-esque meelee fashion if you get too close, so kill them with your shotgun and collect the batteries and medkit found by the dead marine. Then go back and use the button to open the door.
Behind the doors will be four more pit drones hanging out in a car repair shop. Kill them, grab the battery in the far left corner, and continue to your right. Two more pit drones will attack you, having somehow neglected to attack the scientist hiding in the back. He'll complain about "you soldiers" and the aliens. Either ignore him or kill him if that's your sort of thing and go through the elevator doors.
Corporal of the Jungle
Carefully make your way down the ladders in the elevator shaft to the bottom. Enter the elevator on the other side and climb up to the top of it to reach the floor below the one you were just on. To your right is a locked door, to the left is a puddle with an electrical wire in it. Use the crates to circumvent the puddle. When you're on the other side, turn left. Behind the gate is the power unit - turn it off to stop the flow of electricity in the wire. Go straight down that hallway, crouch-jump over the crates, and return to the elevator shaft through the other side of that locked door you saw earlier.
From the bottom of the shaft, climb two of the yellow ladders. From there, you should be able to jump from the platform to a dangling cable in the middle of the room. Unlike Gordon Freeman, Corporal Shepard can climb ropes and the like (but would you rather be able to climb ropes or have a doctorate in theoretical physics from MIT?). Climb this cable until you're a little above the other elevator, swing back and forth, do your best Tarzan impression, and jump onto the elevator. Inside the elevator are two batteries; once you've got those, continue down the hallway to your left.
Weighted Companion Crate
Down the hallway you'll find a locked door and a crate. Looks like you'll be taking yet another trip through Black Mesa's ventilation system. Push the crate over to the vent, break the grate, and crawl in. A scientist is "sleeping" at the end of the tunnel. You'll pass a harmless steam vent, but won't get much further when there's an explosion that rips the vent in two. Crawl down into the gross water, and turn around to find a bullsquid behind the fallen vent. Shoot it with your pistol before it has a chance to squirt you, and head back there to collect pistol rounds and machine gun ammo from a dead marine buddy.
Turn around and head back, sludging through the water until you come to a large hole in the wall. Go through it and through the doors to your right, right back where you started. That metal crate has just become the very first companion cube. Push or pull it through the doors over to a vent next to that hole in the wall, and turn right inside the vent to get a battery and visit your friend the sleeping scientist. (Spoiler alert: he's not sleeping.)
Back out through the vent you go and push your crate over to the closer barricade. Crouch-jump from your crate to the trash barrel and throw a grenade through the broken window. The room will explode a bit more than you'd expect from one of your hand grenades, but it's created a hole in the wall for you and your crate to go through. Bring it through the room and to another vent on the other side of the barricade. Here you must bid adieu to your faithful crate; continue on without it through the vent, killing the surprise headcrab around the corner.
Reunited, and it feels so good
Drop down out of the vent and peer into the hole in the ground. Before you jump down, go around the corner to find a medkit and overhear some of your colleagues chatting - you're not alone in this place! Go through the hole in the ground to be greeted by a scientist and a few batteries for your vest. (You can listen to the scientist's dialogue if you're really bored.) At the back of the room is a sparking wire and a power box; turn off the electricity and climb the wire.
To your left when you come up is a dead scientist and security guard, along with some ammo and a satchel charge as well as a radio. Use the radio to talk to your friends, who tell you they've been left behind as well and are going to explode the maintenance door to let you in.
They'll chatter on about Freeman while you realize you never actually spoke a word into the radio - they just knew who you were anyway. From here on out, you'll be able to have grunts follow you if you'd like, similar to the security guards and the scientists. There are different types of grunts, as you'll experience, and they'll often be needed to access areas. Have the engineer - the marine with the pistol, not the machine gun - follow you over to the elevator door, which he'll cut open for you. Engineers are really good at blowing up stuff. That's about all they're good for. Anyway, wait for him to open the door and enter the elevator. (You can go back and get the other marine if you'd like, but they're about as useless as security guards were in the base game and when you put two of them together, they'll obnoxiously gossip with each other.) The elevator will take you to the next level.