If you've already got the museum and enough progress, you just start at step 3 below. I found brewster on the first kapp'n tour after talking to blathers. Also found gyroid on that same island. Pretty easy.
Make Sure You've Upgraded Blather's Tent to the museum..
Make sure your Resident Services is built and have K.K. Slider visited your island. Also make sure you donate fish, fossil, bug, and piece of art to the museum to trigger the mission to search for Brewster.