How do the different federated software interact with each other?

Hello everyone.
I am relatively new here on Lemmy, and the Fediverse, and there is still a lot I am trying to learn.
I think I understand the general theory of how the different instances and communities work here on Lemmy, but I'm struggling to understand how the different federated software interacts with each other.
For example, I understand that it is possible to follow a community, commenting on its posts, or a user subscribed to Lemmy even from Mastodon. Similarly, it is possible to follow an author on Write.as, again through Mastodon.
What I wanted to understand is what software in the Fediverse interacts with each other, how, and how do you get them to interact.
I hope someone can help me better understand how things work, as I find the idea of the Fediverse absolutely fascinating, a real breath of fresh air in the modern Internet landscape.