I'll try to help! Once you donate five separate bugs/fish to him, on the 5th time he will recieve a phone call from Blathers. You will then be given a tent to set up for him. He should move into the tent the next day. After that, speak to him and he'll inform you he needs 20 donations before he can open an official museum. Once you've donated enough, he'll let you know and the museum will be under construction the next day!
At one point during Day 1, Tom Nook will give you DIY recipes for the Flimsy Rod and the Flimsy Bug Net. Craft the tools and catch 5 unique critters and give it to Tom Nook.
Once completed, he will give you DIY recipes for the Flimsy Watering Can and Flimsy Axe. He will also call Blathers and ask you to set his tent up. From this point, Blathers should come the following day.