Prerequisite: Check the mail box on the third day
Reward: Basic Fishing Pole, Basic Bug Net
Unlocks: --
There's a ton to see and collect as you explore Coral Island, and you'll need a few more tools to make the most of your time. You'll receive two of them by completing Visit the Beach Shack, one of the earliest quests in Coral Island. Check your mail box after arriving on the island and it won't be long before you get an invitation that will trigger the quest.
Follow the invitation and head to the Beach Shack. The Beach Shack is located on the west side of the beach, to the south of town. Enter the Beach Shack between 9:00 and 17:00 - its hours of operation - and you'll meet Sunny and Eleanor, its proprietors, as well as their son Jim. After a bit of debate they will give you two items: A Basic Fishing Pole and a Basic Bug Net. Both unlock substantial collecting opportunities for the Museum.
Speaking to Sunny and Eleanor ends the quest. That said, you now have two important new items, and no idea how to use them. Time for some instructions.
Fishing
Fishing in Coral Island is fairly simple. Take your Fishing Pole to any body of water - the beach, for example, or the pool near your house - and use it near the water's edge. You'll hurl your lure into the water, and for a while nothing will happen. Remain patient, as this won't be the case for long.
Wait long enough and eventually you'll see the shadow of a fish approaching your lure. Once the fish grabs the lure you need to gradually reel it in, taking care not to reel too much. A meter appears on the screen above your catch, and you'll see expanding wiggly lines above and below the meter. When the fish is fighting in the water these lines will expand more quickly, and if they eclipse the meter the fish will get away. You need to slowly reel in the fish, balancing your reeling with its fighting. Fill the meter and the fish is yours.
Though you can fish anywhere you find water, you won't run into the same fish at every fishing hole. You'll need to explore Coral Island, fishing at different times and in different seasons, to collect every fish. We'll cover where and when to catch specific fish in another article.
Bug-Catching
Bug-catching is a bit trickier than fishing, though it's still pretty simple. As you explore Coral Island you'll come across a variety of smaller critters that will gradually become panicked when you get too close. If you move around too much they will flee for their lives. These are the bugs you are meant to catch with your Bug Net.
The key to bug-catching is a bit of patience. If you run up to a bug the meter that appears around it will swiftly fill, triggering a hasty escape. To catch the bug you need to slowly edge up, not approaching so quickly that the bug will flee. Then pull your net out, wait until the bug is within range (if it isn't already), and swing. If the bug is within the cone that appears out the front of your character it will appear in your inventory.
As with fishing, bug-catching is a pretty involved sport. The full details of the bugs you can catch will wind up in a different article.