Instructions
Power on your PS3 and navigate to the Settings menu on the XMB main menu.
Scroll down the list using the D-Pad or Left Stick and select "Network Settings" by pressing X.
Scroll through the list of options until you find "Internet Connection Test" and press the X button. Wait for the connection test to complete and the PS3 will show you the results automatically. The Connection Speed results are located near the bottom of the list.