Dude how do I make that trading machine in the three islands work?

Once you've obtained the National Pok�dex, talk to Celio and then go to Mount Ember. At the foot of the mountain you'll see two Rocket Grunts digging into a hole. One will divulge a password to the warehouse on Island 5 and then notice you eavesdropping. Defeat them to gain access to their hole, and go down to the bottom to obtain the Ruby. Climb out and turn it in to Celio, and he'll give you the Rainbow Pass so you can book passage to the other islands.

Now head for Island 4 and enter the Icefall Cave. Once you've found the HM07, go up the Waterfall in the antechamber, descend the ladder, and go in the hole in front of you to help Lorelei expel the Rockets from the cave. Once that's done, book passage for Island 6 and withdraw a Pok�mon that knows Cut. Leave the town and head for Ruin Valley to the south on the island. When you come to the Dotted Hole, use Cut to gain access and fall through the hole inside. On the floors below take the hole to the north, then the one to the west, then the one to the east, and lastly the one to the south. At the bottom is the Sapphire, but a Scientist will snatch it, but not without giving you the second password to the Warehouse.

Now book passage for Island 5 and locate the Warehouse in the meadow beyond the town. Go through the maze of directional tiles until you defeat the female Admin, who will switch some tiles to allow you to rest and return for more. Once you've taken advantage of that, knock off the male admin and then the Scientist to obtain the Sapphire.

Ruby, inside the cave guarded by the Rockets, just at the bottom of Mount Ember.

Sapphire, use Cut on the door to Dotted Hole on Six Island.

You get the Ruby at Mt.Ember and the Sapphire on island 6 in the cave.

Hope I help

Cross Stinger answered it but I'm adding: If you leave then come back and talk to the scientist again he'll say, " Your not giovoni's son are you? No, you can't be, his son has red hair." (If you have gold, silver or cystal, sound familiar?)