When you enter the frog pond area of any Qu's Marsh, Quina asks to spend some time catching frogs. Quina must be in your party for this to occur. If you agree to let him/her catch frogs, you can control Quina as s/he runs around the pond attempting to catch the frogs that leap onto the ground out of the water. There's no real strategy to this; you just need to be swift.

As Quina catches more and more frogs, Quale appears occasionally and congratulates Quina on his/her progress. The master Qu then bestows items upon Quina as rewards for catching frogs. If you can catch 99 frogs, Quale challenges your party to a battle.The trick to this side quest is to always leave a male and a female frog in the pond. Otherwise, it will take an incredibly long time for the pond to repopulate with frogs. The spawning rate is also much faster if you leave the Golden Frog with a male and a female frog.

One strategy for chasing the frogs is to learn the differences in color. Female frogs are usually a much brighter color than males, while baby frogs are smaller and more olive-toned. You may want to change the Contrast on your television or monitor to distinguish more easily. Avoid chasing baby frogs, because they will grow up to become adults and will be much easier to catch then.
Quina can learn Blue Magic abilities by eating Sahagins or Gigan Toads in Qu's Marsh. You can learn the reliable Frog Drop ability by eating a Gigan Toad. Frog Drop has a 100% success rate and the strength of this ability is determined in part by how many frogs Quina has caught. The damage follows this formula:

Quina's Level x (amount of frogs) x 100 = HP Damage

For example: If Quina is at level 50 and s/he has caught 100 frogs, Frog Drop will cause 5000 HP damage.