The Way Out
Take the path the two zombies were previously blocking and you'll find yourself in an underground tunnel filled with enemies. These enemies are very difficult so be careful. Zombie Dogs can poison you, so take them out first with PSI Freeze. If you are possessed, just continue on. You'll come across a boss.
When you defeat the Barf, exit the cave and you'll be in Grapefruit Falls!
 Grapefruit Falls
Just outside is a man who sells food. Stock up on Croissants and Calorie Sticks because you might run into a difficult enemy up ahead. Also, directly above the man is a Magic Butterfly spawn point. Repeatedly re-enter the area until your PP is completely full before moving on (heal yourself as well).
You'll encounter Red Antoids up ahead. These enemies are very dangerous with bite attacks that can seriously damage you. The Armored Frogs will be difficult to take out with bashes, forcing you to use your PP to cast PSI attacks. The hardest enemy is by far the Plain Crocodile. If you encounter one of these be prepared to PSI Special it immediately. They are very strong and will tear you apart at lower levels. Pick up the Protein Drink and the Bomb on your way north.
Enter the cave up north. Inside you'll find a Bottle Rocket and an enemy called the Violent Cockroach. These roaches are very easy to kill, so just bash them until they are destroyed. When you exit the cave you will be in Saturn Valley, home of the Mr. Saturns!
 Saturn Valley
The first thing you should do is head to the hospital to get rid of any status effects you may have (including Possessed) and to revive any fallen party members. Then rest at the hotel for free. Both of these buildings are the first two you will see upon entering town (the left one is the hotel and the right one is the hospital).
On top of a ladder to the right you'll find a Rust Promoter. Enter the cave to the north (the one with the ladder) and you'll meet four Mr. Saturn's inside. Talk to them all. One of them mentions giving you something, so you should remember him for later. Another Mr. Saturn will tell you the secret of how to get into Belch's base. If you do not talk to him, you won't be able to progress.
Find the Saturn Valley store and stock up on Silver Bracelets and Great Charms for everyone who doesn't have one. Buy a Red Ribbon for Paula and some Peanut Cheese Bars for the party. Save your game, you've come a long way.
 Getting into Belch's Base
Head back out to Grapefruit Valley and walk north and behind the waterfall. Remember what the Mr. Saturn told you about getting into the base? Push up again the wall behind the waterfall and someone will ask you for the password. At this point, do not touch the controller. Do not move Ness or check the status at all. In fact, take a break and grab a quick snack or use the bathroom. You have to wait three full minutes without doing anything before you'll be given entrance.