After you pass through Youngtown and learn to Teleport from the Garricksons' baby, you reach the Swamp.
Explore The Swamp
When you are ready to move on, go east from the center of Youngtown and you will arrive in The Swamp. After you cross the first bridge, go north and cross the bridge there. Then go north and you will eventually find another bridge, so go across it. Go north again and cross another bridge, then go east, then southeast. You will find a shack.
Check on the shaking trash can. After some dialogue, if you didn't use the phone in the Healer's house in Snowman and tell Ninten's dad the player's name, you will be asked to do so now. You can enter your full name, or your first name, or some fake name, or a nickname, or some famous person's name, or whatever you prefer.
You can go into the shack to heal up for free. You might want to spend some time in this area to level up. The enemies are stronger as you go into the southern part of the swamp. You can use 4th-D Slip (a.k.a. Dimensional Warp in the fan translation) if you don't want to fight.
When you are ready to continue, leave the shack and go southwest. The path will start going southeast for a little while. After that, go west, then southwest, then south. Eventually you will find a bridge. Go across it, then go south, and go east when you can, then follow the path to another bridge. Cross it and go east. When you can't go farther east, go northeast to find another bridge. Cross it and go north. After a long walk north, when you can't go farther north, go west to cross a bridge. You are now in Ellay (a.k.a. Valentine in the fan translation).