When I was playing the game I found deep dungeon by playing all sorts of side games. Like finding Cloud and all sorts of things. If you don't know how to find these games they are easily found in the bars and rumors section. If you find a good one they'll have you go somewhere and what not. The best way to find all these is to get right up to the part of the game where you're about to enter the Monestary for the last time, but instead of going on turn back and finish all of the jobs that you can find and then when this is done go to the rumor section and follow up on any that look suspicious. When your done with these the deep dungeon will appear after you battle a monster for an extra Zodiac Stone. This will turn in to the Deep Dungeon. Then there are like seven or eight levels of the Deep dungeon and the only way to go on is to find an exact spot on the battle feild that leads deeper. When you find this spot there will be a message.