Pendulum's Lab
You will see a woman near Pendulum's Lab who will be sad and crying, but she will tell you what you need to do. She will enter the lab and you will have to follow her. Once inside, turn right and you will see her again. Then she'll hand you a mission that you can read in the inventory menu; this mission will help you learn more about the future machine.
Future Machine
To activate the future machine once you are in Pendulum's Lab, first go left, then down and finally right and you will locate the power supply for the machine. This will look like a giant plug. Every time you want to use the machine, you will have to push this plug in to activate it. Then walk to the back of the future machine and go into where it is blinking with a blue color. You will see a terrible future and you will also find a much-older version of yourself there. Talk to him, and he will provide you with a handheld version of the time machine that looks like a stopwatch.
Fixing the Future
In the future, signs will indicate that something has gone wrong to create such a bad future. Something in the past caused it to happen, and you need to go back there and fix it. You will be able to go back in time and go to different places in any order you want, but you will need to find items and return them to various people to fix things and change the future for the better.
Time Tangled Medallion
When you bring back the various items the time machine will always turn partly green as you do so. There will still be items for you to retrieve, however. When all the items have been collected and returned, it will turn completely green. When this happens you need to return to the lab and go to the future. You can do this by using the air lift tube and also the monorails. They will bring you to the home of your future self. Then talk to him and you will get the Time Tangled Medallion in the game.