You don’t get logged in to other accounts. Just follow people at their address, like you’d send an email. The server does the rest.
If your question is about finding people to follow, that’s another matter. Folks on other instances won’t show up in your searches unless someone on your instance already follows them. For popular people, that’s usually no problem. For others, you might get their address from their web page. In any case, once you have their address, you just… follow them. No matter where they are, follow them from your instance and it just works. You don’t have to “log in” anywhere else; that’s the “federated” part of the fediverse.
What’s most fantastic about it is that you can often follow accounts on entirely different platforms. How well this works depends on how well the platform supports the AP protocol, and fundamental models of data. But you can easily follow PixelFed accounts from a Mastodon account, and it works pretty well. It’s as if you could follow Instagram accounts from your Twitter account; that’s the killer feature of the Fediverse, IMO. Discovery is still clunky, and how these things interoperate in “World” can be kludgy. But the possibilities are really very revolutionary.
The first thing Jobs did when he returned to Apple was slash the product line down to just a couple of products. I guess that lesson was forgotten.