There are a couple of reasons one might connect a PlayStation 3 game console to a laptop computer. The PS3 can link up to your computer through a wireless connection. You can then access your computer's hard drive and its videos, music and photos from the PS3's menu. You could also connect to the computer to use it as a TV monitor for playing the console. These two connections are entirely different.
Go to Settings in the PS3 menu and scroll down to Network Settings. Go to Internet Connection Settings and select your wireless router from the list of available connections. If the router has security, you must input your password. Internet Connection in the Network Settings list will say "Enabled" once you are connected.
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Link the laptop and PS3 together through a router if you have one. Connect both the console and computer to the router with Ethernet cables. This is needed for a PS3 with 40 gigabytes of memory and that does not have Wi-Fi.
Connect the devices directly with a USB cable. Use one of the USB-style ports the PS3 uses for its game controllers. This requires a USB cable with two thin connector plugs.
Connecting to a Monitor
Purchase an external video capture card for your laptop. This device will connect to the computer through the USB port and will have both composite and S-video connections.
Connect the capture card to your laptop. Insert its included CD-ROM into your disc drive and install the software on it that allows the computer to recognize the card's drivers and includes a video viewing/editing application.
Attach the PS3 to the capture card using the console's RCA composite cable. Open the video application and turn the console on to view it in the program's screen.
Locate and click the application's "full screen" button to enlarge the game screen to your full monitor.