Golvellius begins with the hero, Kelesis, entering a cave. A wise woman inside gives him the Long Sword and Zest Boots and sends him on his way. The Long Sword will be your only weapon for some time, and the swords that come after it are used in exactly the same way (though they deal more damage per hit). Learn to use it well in the dungeon ahead.
There are a total of nine dungeons in Golvellius, and this is the first. It differs from the rest in two important ways: first, there is no boss at the end; and second, you cannot leave once inside. That's not an issue, since there's nowhere else to go anyway.
You will notice right away that Kelesis only faces to the right. There is no way to attack enemies on your left, and enemies will push you in that direction when they hit you. Keep this in mind as you venture through the dungeon, especially in later dungeons where being pushed to the left side of the screen will eject you from the area entirely.
Kelesis can jump and crouch, and can use his sword from any position. You'll have to crouch to hit most enemies in side-scrolling dungeons, since they are low to the ground. The Red Snakes don't pose much of a threat, and go down in a single hit, but Basketworms are hardier and will relentlessly move left, pushing you back if you're in their way. Although they have 3 hit points, one sustained swing of your sword at close range can take them out (see the Game Mechanics guide for details on sword use).
The first real threat of this dungeon is the Giant Snake that you will meet in an open room near the end of the dungeon. Giant Snakes appear in many side-scrolling dungeons, and always follow the same basic movement pattern (jumping up and down). In this dungeon, they will fire smaller Red Snakes at you, but later incarnations have more dangerous forms of attack. Your best bet is to find a position on the floor near the Giant Snake's landing spot and hit it with a sustained blow each time it lands. In addition to being a sort of sub-boss, Giant Snakes are notable in that they drop a large number of healing talismans, which are often useful to restore your energy before a boss fight in later dungeons.
Shortly after the Giant Snake, the path will branch for the first and only time in this dungeon. Both the top and bottom branches lead onward, but the top branch is notable because it has a destructible block which will spawn three Red Snakes when you hit it. You'll find blocks like this frequently, though not all of them contain enemies.
The dungeon exit is just past the branching paths. Once you're through, the game proper begins in Despa Valley.