In a browser, visit a Lemmy instance’s main page. The admins are listed in the sidebar. Note their usernames.

Still in a browser, go to your home instance and login. Hit the search magnifying glass in the top right corner, and do a user search for whichever admin you want to message. You may have to type in their whole ID in the form @exampleuser@instancename. When their name comes up in the search results, click on it and you should see a “Send Message” button as part of their profile.