How do you get the eon ticket and what is it. And also how do you get..

Eon ticket is the ticket you need to get to southern island where the other Lati_s is resting and protecting the soul dew.

Cheat,trade,nintendo event.

The eon ticket alows you to go to southern island to catch the other "lati" If you said the Pokemon on the tv was blue, you'd find latias on southern island. If you said it was red, youd find latios on southern island. To get the eon ticket, you must get it improted from a nintendo event OUTSIDE the game. To get deoxys, you must get the aurora ticket which is also in a nintendo event OUTSIDE the game.

To get the Eon Ticket you need a cheating device or to attend a Nintendo Event, but never the less it gives you the chance to catch the other legendary bird in this game.

To get Deoxys you need a cheating device.

You need cheat codes, the tickets help take you to another place by ship.

You got to use a action replay/gameshark.

I can't believe no one mentioned that you can easily get the Eon Ticket by trading records with someone who has it in their inventory in Ruby/Sapphire/Emerald. It still won't do you any good until AFTER you've caught the first Lat you picked though! That's the only ticket you can get that way though.
The tickets you get from codes often don't work, but warp codes will-that will probably be the only way to get Deoxys-an AR with a Birth Island Warp Code, plus how to solve the puzzle(I posted those instructions somewhere in the AR codes section for Emerald long ago). AR-Action Replay-is a cheat device you can get at Walmart or game stores for $20-$25 that allows you many additional features, in case you aren't familiar with them, and you can put in codes or use the ones it comes with.