Ain't a dumb question at all! It actually takes reading the ActivityPub specs to answer it, so no surprise if you didn't get it just from reading the landing page ;)
The answer is: it'll happen automatically. Just search for someone's handle, and your server will talk to that other server. When you follow that other users, your server will start federating with that other servers.
Note though that servers might block each other. For example, many Western servers block Japanese pawoo.net, since it allows posting lolicon. Western servers don't want this content in their timelines and caches, so they block it. If your server blocks another.social, you won't be able to follow anyone on there.
But your question also hints at a real problem with Fediverse (of which Mastodon is a part), which is: each instance only sees a subset of the Fediverse. Thus, searching by hashtag will only get you a subset of all posts that contain it. Full-text search is even more complicated.
Gotcha, thanks for the info. That does seem like a real problem, and I do see the complexity of the issue. Are there any current proposals for tackling it without adding centralization? Or do we just acknowledge/accept that that's a tradeoff?
As far as I can tell, Fediverse embraces this as a privacy feature. (It's more of a bump than a roadblock, but still.) I'm not aware of any projects to fix this (although I'm not very immersed into Fediverse development, so maybe check https://fediverse.party, they have a list of Fedi projects).
Theoretically you could layer something on top right? Something that consumes and publicizes everything. And then I guess you come full circle back to centralization but at least you could potentially view and search both a "local" and "global" feed.
I don't understand the system well enough to know if this is a dumb question or not.