Instead of making a traditional step-by-step walkthrough, I decided to with a simpler version: Telling the hard parts
Opening the vault is as simple as it is: Start the 3 engines. They are all self-explanatory to find, if you have trouble starting the engine with the yellow light, read below.
Here, a player must enter the box while the button (next to the control panel) is triggered and die in there. If you are playing alone, enter the box and shoot at the button. After someone dying in there, the engine unlocks and you can start it.
I'll keep it short: 95140 and press the large button
Put the triangle on top of the box that says 3, the square on the 4 and the shape with 5 sides to the 5. The numbers indicate how many sides the shape has.
Crowbar the door
Starting the gas pump is simple: Just find the 3 keycards and attach them to the panel next to it and it should start up. They are hidden all over the place so keep looking!