When meeting Spekkio for the first time, he will explain that there are four types of magic: Fire, Water, Light, and Shadow. Crono's party has magic in them, which allows Spekkio to grant them magic. Crono (Light), Marle (Ice), Lucca (Fire), Frog (Water), and Magus (Shadow) can all learn magic, while Robo and Ayla cannot, due to Robo not being a life form and Ayla existing before magic was created. Ice is counted as another type of water magic when fighting something that is only affected by water or not affected by water.
There are two Techs that Frog can learn that are Water-based.