What is the simplest way to test a plain socket server

Depends on the kind of tests you want to run? If you want to test establishing a connection and sending some data I can think of two simple tests. Use netcat (nc) to "echo" some data into a remote socket, or use telnet to connect to it interactively.

If your server is listening on foobar.com, port 1234 you could test it like this:

bro@host:~ $ echo "Some data to send" | nc foobar.com 1234

Same address/port as above, but make the session interactive:

bro@host:~ $ telnet foobar.com 1234
Trying foobar.com...
Connected to foobar.com.
Escape character is '^]'.
Type some data to send here