Gather your wits and courage because your about to be thrust into new territory on the World Map! After the Siren battle your characters might be a little winded, so let them rest in a tent for the first time in the whole game. This also might be a good time to do some stretching exercises yourself: those thumbs control the fate of an entire world you know, so it's not something to be taken lightly.
After you are completely limber, continue southward down the coastline to the Town of Carwen(don't be afraid to explore a little yourself as you can't get lost!).
From the residents of the town you'll learn the following: 50 years ago flying dragons were used in battle, but now there is only one left and it is King Tycoon's dragon; The Kingdom of Walz is to the south of Kerwin and it has the Crystal of Water (Walz amplifies its Crystal with a machine like the Tycoon Kingdom did with the Wind Crystal); You can't use boats to reach Walz, but with a flying dragon there would be no problem; A dragon was seen heading to the Northern Mountain which happens to have on it the infamous purple people eaters! Uh, I mean, the poisonous purple flowers that cure dragons; and, something random, lizards and hibernating animals are very weak to the cold.
To get access to all of these quotes from the townspeople, you need to talk to the lady in the centre of town first, and then head upstairs in the Pub to meet with a guy who tells you about the dragon. You'll know you're in the right place when your party splits apart. Next, go and find the piano, which happens to be in the Pub, and play a two handed scale up and down very badly.
Lastly, go do some shopping! Pick up a Long Sword for your Knight, a complete outfit in Bronze (also for the Knightly inclined), some Cotton Robes for the Mages, and whatever spells you don't already have. This will be last time I'm this involved in the shopping debacle. This is because of the variety inherent in FF V's battle system. You may have your own favourite party, so I'll only make general comments on the items from now on.
Before you leave Kerwin and head for the North Mountain, be absolutely sure to pick up the Ice Rod (and the Antidote). The Antidote is in one of the barrels in the centre of town, but the Ice Rod (a really great weapon for your Black Mage at this point in the game) is a little more elusive. Essentially, it is under the Item Shop. From the Antidote, head to the right and then down; it's in one of those boxes that are just barely in view. There's also some money in one of the barrels in the North-East section of town, but a guy is in the way. Just remember it for later.