The incomplete tutorial doc/tutorial.md has some very simple examples of a TCP server.
The apps/ directory has some more complete examples of TCP servers and clients, like apps/memcached - a simple memcached-like server, and apps/seawreck - an HTTP workload generator (client).
Seastar itself also includes in src/http code for an HTTP server and client.
You can also take a look at real-like Seastar-using applications (like ScyllaDB) on how they use Seastar. Although these are big projects and finding things (like the server code) in them may not be easy, you will know that what you are seeing there is real working code, and maybe even learn some useful tricks.
We definitely need to finish the tutorial and make it into a usable Seastar book :-(