Ok, it does take some doing, and hopefully the fediverse devs might figure out a better hand-off, but this is SOP in the fediverse right now:

1. Search for the server you are interested in.
2. Go to the server page
3. Go to the upper right corner where the server is identified. In the blue field, you will see: “You are not logged in. However you can subscribe from another Fediverse account, for example Lemmy or Mastodon. To do this, paste the following into the search field of your instance: [identifier]”
4. Copy the identifier.
5. Go back to your home server and paste the identifier into the search field
6. The server in question should show as a search result.
7. Click on the link within the search result.
8. You should be redirected to the site you are looking for, and in the upper right corner you will see the ability to subscribe to that site.

It’s a few more steps but it is effectively the same process for both Lemmy and Mastodon. Mastodon just has a more compact interface so you can have the information on the same screen.

It becomes fairly easy after a few tries. What I suggest is having two tabs open - one with your server and one where you will be searching for new servers, that way you just need to flip between windows.