Pokémon Mystery Dungeon: Explorers of Time and Explorers of Darkness/Chapter 1: A Storm at Sea

The game begins right after the personality test. You will hear (read) voices calling for you to hang on and not to let go. Apparently, you do let go, and the other voice shouts "Noooooo".

You will find yourself on the beach, as the Pokémon that were told to you in the personality test. You will lose consciousness again, and you'll see a cutscene.

Your partner is in front of a Wigglytuff shaped building. He will chicken out and will not enter the building. He will go to the beach where you are, and see the bubbles made by Krabby. He'll spot you and wake you up. At this point, you're asked for your name. A short time after, Koffing and Zubat will take the Relic Fragment from your partner, insulting him on the way.

He'll ask you if you want to help him, obviously, pick Yes (if you pick No, he'll just ask you again). After the small talk, you'll enter the dungeon.

Dungeon: Beach Cave
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Note: All the Pokémon in this dungeon are water type. So you might have some trouble if you are a fire type, but still not to much trouble. This dungeon is the first and easiest dungeon in the game. With only 4 floors to explore and weak Pokémon you shouldn't have a problem. In order to advance to the next floor, find the staircase. In your minimap, it appears as a blue hollow square.

At this early stage of the game, you don't have a bag, so you can only pick up (and hold) one item. The best on this stage is to collect an Oran Berry (which is a blue berry.) you shouldn't have trouble finding one.

4 Floors below, you'll fight your very first Boss Battle.

Double Boss Battle: Koffing and Zubat
Congratulations! Your very first boss battle!

After defeating them, they'll run away, leaving the Relic Fragment behind. They will be a major pain in the future.

Post-Events
Your partner will talk to you for a while, then ask you if you want to make an Exploration Team with him. Pick Yes, and your partner will be happy. You will be asked if you want to save, and you'll begin the next chapter.