In Animal Crossing: New Horizons, Blathers isn't with you from the start, and when he does arrive, he won't have a museum to begin with! Here's how you assist Blathers to get the museum started.
How can you get Blathers to come to your island?
One of the first things you do is add Blathers to your island. Simply complete the missions given to you by Tom Nook in the game's prologue to position your tent, assist your new neighbors, and prepare for the party by collecting sticks and fruits. You can now talk to Tom Nook about using his crafting table after you've slept and gotten through your first full day. He will give you the ACNH DIY recipe for a variety of items in Animal Crossing, including a flimsy net and a flimsy fishing rod, and will ask you to bring him something you catch. If you bring him a new creature, he'll ask if he can give it to a "mate" of his, and if you agree, he'll reward you with new Animal Crossing items and DIY recipes. When you bring him five animals, he'll get a phone call, it's Blathers!
Where to Find Fish and Bugs
Wildlife abounds in Animal Crossing, however, you must know where to look. Fish can be found in any body of water. Be careful as you practice casting your fishing line to land just in front of them. Fish can take a few nibbles before biting, dragging the lure below the water. Now all you have to do is keep hammering the A button before they're hit.
You should try to catch all of the bugs in a net:
During the day, butterflies will flutter about gently. Snag them in your net!
A moth can almost always be detected by the light outside the Resident Services tent at night.
Snails can be found camped out on rocks, particularly when it rains.
Conch-like shells on the beach can turn out to be hermit crabs at night. Capture them in your net.
When you smack a rock with a shovel, pillbugs or centipedes can appear.
Shake the trees and bagworms and spiders can fall out, allowing you to quickly snag them in your net.
When shaking leaves, take care not to knock a wasps nest to the ground. Using a net quickly to trap the wasps before they bite you!
At night, beware of tarantulas, which can chase and bite you if they spot you... However, with fast reactions, you can catch them!
How do you know if you've snagged anything new? If it's a new catch, your villager will yell "Yes!" when they show it to you. If it isn't, they'll just get right to the point and say what it is. You can also look in your NookPhone Critterpedia to see what you've caught and donated to him.
With Blathers on the way, Nook will hand you a tent and ask you to find a location for him and any museums he wishes to build. Consider the scale of the venue, which is much larger than the tents you'll have pitched so far. When you're satisfied with the location, simply set it down, and Blathers will appear the next morning. During this time, Tom Nook will not allow any more donations, but you can try to save them (you can put bugs and fish in small boxes) and give them to Blathers when he arrives.
Blathers is on an expedition to show the value of constructing a museum to collect knowledge about your island. He needs to catch 15 more insects, fish, and fossils to explain this! But how can you collect fossils if you don't have a shovel? Fortunately, Blathers will give you the DIY recipes, not only for a shovel, but also for a river-vaulting pole so you can explore more of the island. Continue collecting items for Blathers until he has enough to justify building a museum. At this point, he will no longer accept donations; construction will begin the following day, and the museum will open the following day. What can I do in the meantime? You should have probably moved from a tent to a house by this stage, so keep any newly found fish, insects, and fossils in your home's built-in storage so you can donate them once Blathers' museum is up and running. At this point, he will, luckily, begin accepting bulk donations and requests for fossil assessment.