Portal 1, few things to know 1st:
Your a girl whose name is Chell
You have a dimensional portal that can help you get to tough places
There is a talking robot throughout the game
you go through tests.
There is a hidden character called 'Rat-Man'
You wake up in a 'sleeping' Chamber that has a toilet, bed, radio, and a clipboard. You are greeted by GLaDOS, who tells you that you are in Aperature science as a tester. You enter a portal after 1 minute after getting up from sleeping. You then go through a few tests and eventually get a Portal gun that can shoot only blue portals. Later on, you get the Orange portal as well. During this, GLaDOS says that at the end of the tests, you will be rewarded with cake.
A couple of tests later after getting the portal guns, you meet a companion cube that has a heart, that you use for the test chamber. When you complete the Chamber, you have to toss away the cube to continue on the testing.
When you complete the tests (19 tests overall in the story), you find out that you are slowly entering a batch of fire that will kill you. You use your portal gun to escape it and try to get out of there. And yes, this does mean that the Cake is a LIE. During your time trying to find a way out, you find out that the place has been abandoned for ages, and that GLaDOS probably killed every worker.
You eventually find your way to GLaDOS'es chamber. When she's saying that someone going to get Chell in a while, a purple core falls down adn you throw it into a fire pit. After that, GLaDOS then gets a little re-write and GLaDOS voice get's lower. GLaDOS then tells you that the core you threw away was a neurotoxin repel core that stops GLaDOS from using neurotoxin again, due to the fact that she used it once before, she activates it, and you've got 5 minutes to get rid of the other cores on her.
After you get rid of them, the top of the chamber is breaking apart and you start to fly up there. You wake up on ground and you black-out.
In 2010, Vlave updated the Ending to make Portal 2 be part of the story. In this new ending, you wake up on hard concrete, and you are being pulled away by a robot (You don't see it, but is presumed to be Rat-Man as a robot).
Just a little info about Portal 2, it is centuries later and your still alive due to the fact that you were frozen, and GLaDOS is still alive.
Hope this help. :)