When you open the door, it falls open...like a spring or pully is broken

Go to Partsselect.com and enter the model number of your dishwasher. On most dishwashers the model number can be found on the door I believe. This will show you a diagram of the parts a they often have a video on how to install the new part. Hope this helps.

There are springs and pulleys that assist the door. They use a nylon rope that is very thin to connect the pulleys door and springs. The rope is most likely broken.

Could be. Yet you may only need to adjust the springs and not replace them.. In case you have roll up/ sectional garage door, it should be quite easy you need to release the traveler from the rail so you can open and close the door manually/by hand then, while open the door on the knee level leave the door. If it falls down the springs need adjustment.
In general the door should stay at the same position on every stage it is while pulling it up and down.
If the door falls/ closes down not enough tension on springs, if door opens up too much tension on springs. If door acts funny.like close when close to the floor and jump up when its futher more open, it means that you don't have the matching springs for the weight of your garage.

Falls open when? This unit wom't operate unless the door is secure so I assume you mean the door assist springs are disconnected or broken and the door just falls heavily to the open position after you unlatch it from the closed position. Try these, part 18 here

http://www.searspartsdirect.com/partsdirect/part-model/Kitchenaid-Parts/Dishwasher-Parts/Model-KUDI01FLSS3/0593/0130000/W0503111/00007

should attach to frame in an easy to distinguish hole or slot and to door hinges, number 2 here

http://c.searspartsdirect.com/lis_png/PLDM/W0503111-00001.png

Broken spring.

You probably have a broken torsion spring. If you have a spring on a shaft above the door (usually 2 if it is a double door) then you have a torsion spring. From this shaft you have a 2 cables wound on a drum going down to the bottom of the door. If it is a single door, then this cable will be loose. If you have a double door, then most likely one spring is broken. This allows the door to open slightly, until one side is trying to lift(good spring) and the other side cannot (broken spring) Unless you are an EXTREMELY CONFIDENT DIYer then you should leave this do a door repairman as winding a torsion spring is dangerous, and can break bones or even kill. Now if your door has extension springs on each side of the track,with a pully and cable, then these can easily be replaced yourself. Check that cables are connected to the springs and the door and that one didn't break or come loose or cable off pully and binding.

The side spring springs could have unhooked. Some springs connect to a nylon rope that slides over a plastic guide. The rope could also have snaped or slipped off the guide. You need to open the sides (normaly the back first) to check. This is easy to fix if you have the right tools...

there is springs on left and right side held by string and spring. one is broken.letme know how it turned out.

I think any parts person would recognize it by that name.

It's a fairly simple fix.

The one you have may just be loose on one end and not broken -- check that before you buy one.

There is normally 2 heavy springs & cables that control the "falling" of the door located in the bottom of the machine or it the door itself. Sounds like one (or both) have snapped.