After contracting with Maxwell and getting the treasures from Moria, you search for Edward.
In Alvanista castle, talk to Runeglom/Lundgrom in the Magical Research room. Afterward, go into town to buy supplies and food.
Leave Alvanista, cross the bridge to the left, and keep going west to find Edward's house. Knock on the door to learn where Edward went.
Southwest From Edward's House
Before following Edward, go southwest from his house to find a camp where you can get a new skill for Cless/Cress.
Go east, past Alvanista, then go south to find a dock. At the dock, talk to the captain to go to Freland.
Go east from the Freland dock and go into Olive Village. After the cut scene, leave Olive Village and go east and south to reach the first oasis. Talk to the person and open the chest (Rune Bottle). There is another chest next to the southern tree that contains a Flame Mantle.
Leave the oasis and go northeast to the next oasis. Talk to the old man and open the chest (Medicine Bottle).
From there, go north and west to the final oasis. Don't talk to the person yet. First, open the chests. There is a chest visible under a tree that contains a Life Bottle. Go down from that chest to find another chest under the trees. It contains a Mental Ring. Now talk to the person and you will return to Olive Village.
Olive Village and Freland Desert
Go into the inn and talk to the innkeeper. Rest if you wish, then buy some Dark Bottles if you don't have any. Leave the village.
When you fight the Basilisk, have Klarth/Claus use Maxwell, have Arche use Thunder Blade, have Cless/Cress use Lightning and Tiger Teeth, with Mint healing at all times.
If you have trouble finding Basilisks, go southeast from the village and walk around the area just northeast of the southern oasis. Basilisks seem more common in this area. Use a Dark Bottle to encounter monsters more frequently.
After you have won five Basilisk Scales, go back to town and talk to the innkeeper. Stay the night.
Your next destination is Alvanista, where you can get permission to visit Ymir Forest.