After the intro, go to the right. Talk to your friend Dry. Go outside, go back and talk to Dry again. Go outside and go down, and right. Talk to the chicken. Go north a few screens and talk to the dragon. Go three down and two left. Enter the middle door. Go downstairs, and take the right exit. Take the heart and go back to the screen with the three doors. Go right all the way, below the border of rocks. Keep walking and you'll see a potion, take it. Again back to the screen with the three doors. Go down and right, and talk to the fountain. Take a sip. Go left and down and enter the house. Talk to the man. Go back to Dry and ask for some cash. Leave and go two right, one down. Talk to the guy in the boat. There's a secret here, just explore the right edge and find the chest ;)
Go four left, one up. There's a small cut scene, then talk to the fish. Go two right, one up and use the door. Talk to the pig. Exit the church and go two left. Walk to the pig and you'll be warped. Use the stairs and save. Go up and kill the monster (30hp). Go left and talk to the pig, he'll give you the weapon. Arm it. Use the stairs and leave the church. Go two left, one down and talk to the fish again. He'll tell you the riddle: Cave entrance to the north? Go west and west. Count the rocks. Die and count some more. The total of the sum is where it is.
The cave entrance to the north is the cave entrance near the dragon shopkeeper, so go there. Go west and west (left twice) and count the rocks on that screen (2). Then die and count some more. To die, go to Death, the guy in the boat. Count the rocks here (4). The sum (6) is where it is. Now find a screen with six rocks. Now go left twice, down and right twice. Now go all the way down and you'll see a screen with six rocks. Go to the corner, there's the invisible entrance. Listen to the 'singing' girl, then go a bit down and right. Use the teleporter and save. Read the sign if you like, then go left.
Now this part will take some time because you'll have to kill all the enemies to proceed. So, follow the path and use your boomerang to kill all the enemies. If you can't go down anymore, go left all the way. Use the stairs and walk up all the way. Save and go up. Kill the monster and go left, use the teleporter. Open the chest. Use the middle teleporter in the first row.
Go to the guy with the T-Shirt and buy it. Go to the dragon and sell it. Go three left and six down. Talk to the fisherman. Go to the chicken and give him the sunburn lotion. Go to the T-Shirt guy and talk to him. Go outside and go four right, one up and walk into the girl. Go up and walk into the chest. Now walk into the fourth chest and take a trilobite. Go back to all the chests and walk into the most left chest. Talk to the guy again. He doesn't want this trilobite so go to the chicken. Go back to the guy and talk to him. Then go to the guy in the boat and talk to him. Now go to the dragon shopkeeper and buy the T-Shirt. Go back to the guy in the boat and give him the T-Shirt. Go to the fisherman, he'll give you some fishing bait. Go back to the guy in the boat. Don't argue with him.
Go two left and two down. After the cut scene, go down and enter the left house. Tell Jill Jack hates the desert. Go outside and talk to the pig. Go right and talk to Jack. Go down, and left three times (terrible Private Smith cut scene..) and talk to Jacques. Go back to Jack and talk to him. Go left and down. Talk to Sniff. Now go to the pig church (the door one screen north of Dry's home) and talk to the other pig. Go back to the screen with the Private Smith cut scene and take the pamphlet. Give it to the pig, then go to the fisherman, talk to him. Go one up, and left. Again a long cut scene, then go to the screen with the three doors. Use the middle door, enter the cave. Go to Dry and talk to him. Go back to the cave, she'll talk to Dink, then go back to Dry again. Go back to the cave, go outside and enter the cave again.
Go to the guy in the boat and talk to him. Go to Jill and ask for a bottle. Leave and go left three times and down. Take the rock and give it to Jill. Now go to the most northwest corner of this desert, then go left once. Walk into the knight, save your game and talk to the guy there. Go left and kill the monster. Go up, walk into the heart, the left girl, then the fourth giant. Use the other stairs. Take the hearts and the potions, walk into the knight. Go up twice and walk into the knight. Now you're in the Desert of Lost Souls. You can follow the path or fight your way through it. This is the path: 3 left, 2 up, 4 right, 1 down, 1 right, 3 down, 5 left, 2 down, 3 right, 2 down, 4 left. Use the invisible teleporter in the corner.
Here you are, Greenland :) Walk around and go to the left. You'll see a fountain with fresh water, talk to it. Watch the cut scene, you've finished Dry!