If you are the host, you can either connect to it by typing the public IP or by simply typing 'localhost' if your server is running on the computer you play.
Too many or misused mods, plugins, or worlds can cause server lags. Make sure to install a reasonable amount of plugins and don't create too many worlds.
You need Ethernet connection. Then one created a World. Press Esc and then open to lan. If you are both connected to your Router vie the LAN cables the other.