The basic functionality of the homeserver is only just starting to land, so we're not testing any of the federation aspects yet. The current test suite is just your standard web app integration testing. Take a look at the repository's README[1] for some high-level details, and src/test.rs[2] for details of how it's actually achieved in Rust using the iron-test and diesel crates. The PostgreSQL database used for testing is managed with Docker and Docker Compose.
It's worth noting that the Matrix.org project itself provides an integration test harness called sytest which can be pointed at other HS implementations to check their behaviour: github.com/matrix-org/sytest
