To start this quest you'll need to head to Yardrat and make sure the ability is on your ALIST already. The two easiest ways to get there are to hop on a transport ship or ask someone for an IT (instant transmission) to there. If you've been training on Furiza or The Ginyu Base the planet Yardrat is the stop right after this so it is a short jump.
Once you're there head NW from the landing pad, and continue heading nw to the Temple. SAY YES to enter the temple and being the quest. There is a mini flower quest you can complete before going into the temple but you don't need to. It can be started to the north/northeast from the intersection you approached before the temple.
Optional Step: To get the beautiful flower head north from the Village Square, open the first door to the north, and Volk will run out. Follow the path all the way south, then south west until you come upon a cave. Enter the cave and kill the beast. You'll get the fur and after going north be transported back to town. Head back east to the square and northwest into the temple.
This is a quest area so skip these notes if you want to try it out yourself, however a detailed spoiler is below for your viewing pleasure.
You'll probably want to be about 5 million PL before going in. And make sure that Instant transmission is on your ALIST already and not just greyed out.
From the Temple Antechamber (starting room of the quest) you'll need to go in each direction and answer some simple questions. See above Yardrat section if you don't know how to get here.
NW, UP, SAY NEUTRAL
NE, UP, SAY NEUTRAL
SW, UP, SAY LOVE
SE, UP SAY FIGHT
Once you have all four sphere go north, up, south and you will get the neutrality sphere. Head south and PUT SPHERE GREY. Return north and GIVE ORB GUARD to head to the next area.
You'll need to complete a speed maze, it is pretty easy, but if you're on mobile or can't for some reason the speedwalk is : qnnnqnenwrnrnwwstywwrnnnw from the Stone Tunnel Entrance, which is one NE from the room you enter.
Follow the path back and then head to the west. Make sure you're in a room where you can LOOK CLOCK and see a description. Type TIME and wait until the in game DBI time is 6'o'clock. When the clock is at 6, WEAR SPRINT. If you wore them before you'll have to REMOVE SPRINT and WEAR SPRINT again. You'll get spammed with a big paragraph and get a Wings item.
Head south to the flaming pedestal and PUT WINGS PEDESTAL, and you'll be whisked along to the next area.
Here is the Space Antechamber. You'll need to head to every corner of the little area and collect all the colorful energy orbs. Don't forget to go to the outside ring and then head up and down. Once you have all 6 of those return to the starting room and go down.
Once you've been transported into the next area head all the way west, then go into each branching room North and then South as you head back east through the area. The answers in order from west to east are, "WHO, HOW, DESTRUCTION, KEY, EVIL, I WILL". After you've answered them all head back to the middle and go south.
In the next are you can go to the rooms in the nw,sw,ne,se directions to get more gear or continue forward to fight Baal. Defeat him and then Instant Destruction. You'll need to then move east out of this room and a little scene will play out, kill Instant Destruction one more time to complete the quest and learn Instant Transmission. And just hope that he doesn't kill you, I've been told it is possible for him to do so and you'll have to repeat the quest...