Connecting to Arduino Ethernet Shield
Your question is kind of trivial, but from what I understood you're typing the IP address (that the Arduino displays on the serial monitor)  into your browser.

First, make sure you connect your Ethernet shield to your router using an ethernet cable. (Now it's connected locally...)

Second, even if you type in your Arduino's IP address into the browser, the browser will return nothing because the Arduino simply has nothing to display, and hasn't been programmed to accept requests.

To actually have the Arduino display something you can try the Webserver example sketch or you can follow this great Tutorial that I found very useful for beginners.

BTW ports are only used to expose your Arduino to the Internet, in other words if you don't portforward to your Arduino, your Arduino won't be able to get requests from outside your local network (Wi-Fi,Ethernet).