1. Talk to Medicham near your base. She will direct you to Lombre, who will then tell you about the Stormy sea. Then Talk to Whiscash to get Dive, which is required to get there.
2. First you need to recruit the Legendary Birds(Their friend area comes automatically with them), then go see Alakazam. He will ask you to go to their friend Area(Legendary Island). Once there, you witness the creation of the vortex stone. Then you gain acess to the Silver Trench(A 99 floor dungeon with Lugia at the bottom)
3. After Recruiting Lugia(Which is REALLY easy), you wake up the next morning to find an unlikely visitor at your Base, Xatu. Xatu tells you of a cave that was created by a shard of the destroyed meteor and is inhabited a "strange Being" A.K.A Deoxys. You can only bring 3 items(+a hold item(X-ray Specs are reccommended) and no team members(send your Highest level one). You need to defeat a Phantom Deoxys on each floor. Then on Floor 20 is Deoxys, who will join if your leader is extrememly high level.
Hope I helped.