Suppose someone sent you a lemmy link like this: lemmy.example.com/post/12345.
Now, you have an account on another instance called lemmy.test, also logged in and want to comment. But opening the original link lemmy.example.com/post/12345 still treats you as being unlogged, because it looks logins from lemmy.example.com, not lemmy.test or any other federated instances.
The solution, for now, is to use the search* function from your instance (lemmy.test) by pasting the original link (lemmy.example.com/post/12345). That gives you a URL that's compatible with your login inside your own instance: lemmy.test/post/98765.
You can do this (or rather, have to do this) with communities or user links too.
I heard there are browser extensions doing this automatically, but haven't tried. Mobile apps should have better support.
* Edit: I remember being able to do this but now its not working. Perhaps something changed? I recommend using browser extensions or mobile apps that should take care of this automatically.
Edit 2: I realized how to obtain the actual working link.