Enter the Orphanage then head through the door on the right. In the next room, go north towards the beach. Watch a cool FMV introducing Ultimecia’s Castle then make your way north, towards the chain. As you’re walking up the huge chain, you’ll see 3 bluish-white doors on the left. Press [X] to leap towards them. Enter the upper left door or the one in the middle to get out. Here’s where they lead:

Upper portal: Region near the Chocobo Sanctuary (Coastal area of Grandidi Forest)
Middle portal: Region near the Centra Ruins (Serengetti Plains)
Lower portal: Region near Deling City (Wilburn Hill)