Yes, you can use it at home on your wifi, or at any public free wifi spots (or even hotel wifi when traveling).
You can use it away from home with no connection as well if you have games, music, or other apps loaded that don't require a constant connection, or for using the camera functions.
You will likely want to create a Google account (free) if you don't have one. The tablet will guide you through when you first use it. That makes it easy for adding new apps, backing up, etc.