Final Fantasy IV/Odin

Fly to Baron
Reaching Odin requires that you be able to fly around the overworld, so it is probably best to attempt a battle with Odin after defeating the Giant of Babil. In addition, you must complete the Cave of Summoned Monsters in order to challenge Odin; otherwise he will simply tell you to come later.

Fly to Baron Castle and enter it.

Locate the King of Baron
Go through the two gates until you reach the first interior room. In this room, go to the right, and up the staircase. Continue through the castle, going through the door in the tower at the back right of the castle. In this next room, go down the staircase on the left, and continue on to the right in this room. When you go down the staircase at the end of this hall, you will find the King of Baron, who will then fight you as Odin.

Defeat Odin
Odin is not too difficult if you have reached high enough levels. His initial attacks are not too strong. However, during the battle he will slowly raise his sword. If you are not able to defeat him quickly enough, he will unleash Zantetsuken, an attack that will kill your entire party. You must defeat him before he is able to complete this attack. Once you have defeated him, Rydia will gain the summon Odin.