It's been quite a while since I've played with a raspi but I remember that you have to write a wpa_supplicant.conf text file with your network ssid and network password and place that on the first partition (boot) of the SD card. That's if you want to connect with wifi. I don't think you need it with an ethernet cable.

If you are running windows you can open a command prompt and type ipconfig to see what deices are connected to your network. Angry IP scanner can be helpful too.

This vid explains how to setup a raspi to connect to wifi