When you first get Quina in your party, it mentions or exclamates that it loves frogs. So, in the Qu marshes around the overworld, there are usually ponds where the frogs gather. Basically when you enter that area, agree to Quina that you want it to catch frogs. Just run up to the frogs and eat them. Frog Catching gets you prizes and a boost for the Frog Drop Blue Magic.

Number of Frogs and Prizes
02: Ore Stone
05: Ether
09: Silk Robe
15: Elixir
23: Silver Fork
33: Bistro Fork
45: Battle Boots
99: Gastro Fork