This is an incredibly short chapter and it really doesn't warrant it's own section. Just follow Alyx through another secret passage into Dr. Kleiner's lab. Just wait around for a few minutes and listen to Alyx and Kleiner talk. Barney should arrive soon and join the conversation.
You're basically free to just look around the lab and listen until they are done. You can play with the mini-teleporter on the table and send the cactus back and forth if you're bored. Barney will open the metal door by the entrance at some point and release your HEV suit (You'll also get to meet Lamaar). Get into the suit and get your first shield energy at the auxiliary charger on the wall when Kleiner tells you to do it.
The alarms are getting louder, so they've decided to speed things up. Follow Kleiner into the teleporter room and watch the scene. As it gets ready to send Alyx out, the plug on the panel falls out. Just pick it up as instructed and stick it back into the panel. When Kleiner opens the safety glass, flip the switch and teleport Alyx to Black Mesa East.
It's your turn now. Just step into the teleporter and watch the cinematic as Lamaar lengthens the gameplay by a few hours. Once it settles down, you'll find that you're stuck outside of Kleiner's lab and you've been spotted by two scanners. Start moving along the catwalk and head down to the gate in the fence below. Just follow the path to the right and go up the stairs to get to a door.