Choice on the Floating Continent
When Kefka seizes ultimate power and threatens to destroy the world and everyone in it, Shadow volunteers to stay behind on the Floating Continent and hold him off while your other party members escape. Then, after getting to the airship, you have a choice to make. Wait for him here and he will show up in the nick of time, rejoining your party later in the World of Ruin. Jump off before he rejoins and he will die, and you will meet Relm on the Veldt later instead.
Meeting Shadow/Relm
The only way to re-recruit Shadow in the World of Ruin is to return to the Veldt and enter the cave there. You will find Shadow there, unconscious, if he survived the events of the Floating Continent. You can then take him to Thamasa to recover and recruit him by betting the Striker at the Colosseum. Otherwise, you will find Relm.
Instructions for the Floating Continent
Escaping the Floating Continent can be difficult, especially if you want enough time to get Shadow back. You have only six minutes, though it doesn't matter if you get there ahead of time since Shadow will always show up with only a few seconds to spare. Equip Wall Rings, so you can survive the enemy's magic attacks, and use Ice and Pearl magic on the boss near the end. Then, walk up to where the airship is hovering and select "Wait!!" and then "Gotta wait for SHADOW." Then you wait until time is almost out.
Connections Between Relm and Shadow
The game does not explicitly establish a connection between Relm and Shadow. However, it is implied in Shadow's dreams that Relm might be the daughter he left in Thamasa as a baby -- she is both a Thamasa native and acts familiarly with Interceptor, his dog who he met in that town. Also, both characters are the only ones who can equip the Memento Ring, which Relm received from her mother.