The MysticTicket & The Aurora Ticket...disputed to be one of the most talked about topics in FireRed/Green

These Tickets can be obtained one way, and one way only. Going to a Nintendo event which has a Wonder Spot (an actual machine in real life), going near the Wonder Spot with the Wireless Adaptor Connected and accessing the Mystery Gift feature of the game.

When doing this, the Wonder Spot automatically sends the game the bit of code which makes a guy in any Pokémon Center on the 2nd Floor give you the ticket. Voila, you have one of the tickets

 
Now you are able to go to the secret Islands. Go to the port in Vermillion and the Sailor will notice your new tickets

Once this happens, you should Always be able to go to the islands, contary to what was previously believed. However you can only do this from Vemillion, from the Sevii Islands you have to go back to Vermillion to do this:

With the MysticTicket you can go to Navel Rock. On this Island there are 2 Pokémon to be found at Level 70. Lugia & Ho-oh:
With the AuroraTicket you can go to Birth Island. On this Island is one Pokémon. A Level 30 Deoxys...the rare Multiform Pokémon.: