If I as an instance owner search & subscribe to another instance’s community, I get “federated” with that community. Does that mean my instance is, or my user is?

When a user on your instance subscribes to an external community, the instance that hosts that community gets a notification about the subscription. Then when new content is posted to to that community, the remote instance forwards a single copy of that content to all instances that have subscribers to the community, including your instance.

Then, when your instance receives it, it checks the content to see if it should send anyone a notification, and does so. It then makes the content visible to people and it will start appearing in the appropriate timelines of your local users (ie, in the “subscribed” and/or “all” timelines depending on the user)

If I want users at my instance to see posts from communities on other instances, is there a way for me to pull those posts in to my instance? Or, how do I get my users to see other communities’ content?

As soon as a single account on your instance subscribes to a remote community, you will get future content from that community.

As an admin, assuming you don’t want to subscribe to random groups just to federate them, you can create a dummy account, find common/popular communities using a site like Lemmyverse, and then subscribe with your dummy account.

You can also point your users at https://lemmyverse.net/communities. That site lets them set their home instance, and once they’ve done so, links to any community will point the user to the community on your instance. And if your instance didn’t have it, the act of someone trying to find it will cause your instance to go and fetch the community and recent content posted to it from the remote instance. Though in this case, unless the user then subscribes, you won’t continue to get future content from that community.

Your instance is the one that federates. However it starts with a user subscribing to that content. Your instance won’t federate normally without user interaction.

Normally the solution for the second part is relays. But that isn’t something Lemmy supports currently. This issue is very common with smaller instances. It isn’t as big of a deal with bigger instances since users are more likely to have subscribed to more communities that will automatically be federated to your instance. You could experiment with creating a user and subscribing to a bunch of communities so they get federated to your instance.