I will not give any hints in conversations, those choices are entirely up to you.
EDIT: I've noticed that since this chapter and the previous one take place in the same place, it's possible to get to this chapter without the water bottle and railroad map. They can be found in the wagon behind the locomotive, in the makeshift 'camp'.
On the side of the console is a clipboard, investigate it. You'll probably start thinking about the pencil leave drawing Clem made earlier.
The next part is (apparently, according to another player) optional, so feel free to skip this block of text. If you leave through the door on the left of the console (to the front of the locomotive), You'll find a car with a walker inside. There's a pack of animal crackers near his legs. Should you look at the walker's seatbelt, you'll get a funny comment from Lee. Open the door of the car, unlock the seatbelt, and use the car's door to kill the walker. Pick up the animal crackers and give them to Katjaa for Duck.
Give Katjaa the bottle of water for Duck.
Talk to Clem, she'll tell you there's a pencil in the RV.
Get the pencil in the RV (it's in the front, in a cupholder).
Get back into the locomotive and use the pencil on the clipboard to reveal the startup sequence.
As of this writing, I'm not sure if the startup sequence is different for every player. Use the main console in the cabin and check the startup sequence for reference. Take note: Number nine is the last one, and it's not inside the cabin. So do everything up to number nine.
Go outside (but stay on the locomotive). On the back compartment, there are a couple of engine doors. Open the left one.
Turn the switch left, then right. The engine should start now.
Go back to Kenny, and talk to him. Use the throttle to start the train, You'll notice you're stuck.
Go back outside and open the second left engine compartment. Take one of the nail removers (it could be possible that the other tools work too).
Go into the wagon, and exit it on the left. On the back is a coupling pin you can pry loose with the tool you just got. Take note that you can't do this until you have tried to start the train, as the shock removes a layer of rust.
There's nothing more to do in this chapter except for some conversations. When you're done, use the throttle to start the train, and the achievement unlocks.
EDIT: Seems I ended the solution prematurely; after you use the throttle there are some more conversational choices (with a couple of 'big' choices) before the achievement unlocks. However, there's no way you can get stuck after this, so all choices are up to you.
EDIT: To negative voters - Please leave a comment on why you thought this solution wasn't good.