Age: 7
Height: 107 cm
Weight: 18 kg
Right-handed
Birthplace: Mist

That's what she is when you first meet her. You killed her mother's dragon - and her mother as well. She attacks Cecil and Kain by calling Titan. That causes an earthquake, and then Kain is gone. Rydia is injured, so Cecil takes her to Kaipo.
She joins him after he protects her from the Baron guards that want to kill her (isn't that awful? She's just a child!).
At first, she needs to learns some spells. At the time she can use both white and black magic. She also knows one call spell - Chocobo.

Anyway. Rydia goes with Cecil, as he has to save Rosa. They meet Tellah, then Edward (after the Redwings destroy Damcyan) and then Rosa (when her fever is cured) joins them.
Rydia hates fire. Remember her home village was burned. But, at Mt. Hobs, she is the only one who can help the party to continue, because of the ice that blocks the way. And so she concentrates and casts Fire1.
Yang joins the party at the top of the mountain. Off to Fabul to protect the crystal. Well, that didn't really work out, right? Kain, you traitor...

Later, the party takes a ship and leaves Fabul, headed to Baron. In the middle of the ocean, Leviathan attacks. Rydia falls off the ship. Yang tries to rescue her. And when Cecil wakes up on the beach, they're all gone. All.
And then Cecil becomes a Paladin and he's with who ever is in the party at the moment. Then you go to get the Earth crystal and save Rosa... blah blah blah. Would've been much more fun with Rydia, but okay. Oh, hi Kain, nice that you joined us. Down to the Underworld - to find some more problems. The Calbrena. And Golbez...

When Rydia returns, she looks matured. She saves the others by calling Mist Dragon.
She tells the others Leviathan took her to the Land of the Summoned monsters. She has some new, powerful call spells. She can't use white magic any more, but knows has learned more black magic while she was gone.

There you are, in the Underworld. But with Rydia's help, it's much more easier. Now to the tower of Bab-il, back to the Overworld, to the cave near Eblan (and later Edge joins you), back to the Underworld, then back to Overworld. Get a walkthrough, I'm not a game instructor.
Anyway. Visiting the Summoned monsters, Rydia can learn more call spells. And more later in the Overworld and on the Moon. And if you are patient and get her enough levels, she will learn some useful black magic like Meteo.
Well, the rest is history. If you have finished the game, you'll know what I mean. If you haven't, you shouldn't be reading this...