This level introduces you to the alien world of Xen and the differences between it an Earth. You'll also get a new weapon.
Lambda Complex Teleporter
Emerge from the vent and to hear a scientist urge Gordon Freeman to jump into the teleporter. To your right are a health station and an HEV recharge station. After using those, go down the hallway and open the door using the button on your left. The door will open just in time for you to see Freeman leap into the portal. There goes your chance of promotion.
Not long after, the teleporter starts malfunctioning and a bunch of alien controllers will start shooting at you. Ignore them, if you can, and run around to the right until the platform the scientist was standing on falls in front of you. Crouch-jump onto it and go up to your very own portal to Xen.
Welcome to Xen
Your bad luck has now brought you to a strange alien world. Should've joined the Coast Guard, Shepard. Jump to the nearest rock island that's a bit to your left. If the jump seems far, don't worry, you'll make it - gravity on Xen is weaker than on Earth. Collect the ammo canister from the dead scientist in the HEV suit and use the alien trampoline to launch yourself up to the next island.
A lab-coated scientist will fall from the sky, screaming, and land on the adjacent island, along with a fun new weapon. Leap over to that platform (save before each jump if you're not confident) and pick up the displacer gun. The primary fire will release a glowing green orb that is guaranteed to cause a bunch of damage to its target. The secondary fire is a bit different - it'll teleport you between dimensions/planets/whatever. That is, if you're on Xen and you press it, it'll teleport you to a place on Earth. If you're on Earth, it'll take you back to Xen. It uses up a lot of charge (60, to be exact), however, so you shouldn't be using it like crazy. Each chapter will take you to a different area if you use it.
If you choose to use the teleport feature, in this section it will take you to the crouch-jump section of the Black Mesa Hazard Course. Near the holographic instructor will be a vortigant; shoot it with your shotgun and jump over the railing. Proceed through the course, taking out the other vort at the end. Get the shotgun ammo from the dead security guard, and jump over the the railing on the left to climb up to where the observation room is. Jump over that railing and smash the window with your wrench to enter the room. A health station will be on the wall opposite the portal, which will take you back to the island where you got the displacer gun.
Unless you're low on health and really feel the need to heal up, I'd skip this and save your ammo for something else.
Lots of Jumping
Continue from that platform on until you get to the one with another alien trampoline on it. Look up and a bit to your right to see two islands fairly close to one another. Aim for the rightmost one and use the alien trampoline to get up there. (Save before making these jumps, just in case!) You should land on the one that doesn't have the houndeyes on it, so you can take those out from a safe distance before jumping to their island.
Use the alien trampoline on the houndeye island to leap up to the tallest of all the islands. From here you should have a good view of the portal to the next level. Save, then jump off the island and into the portal.