It's not surprising that you can't play Xbox 360 games on a computer; if you could, no one would buy the console. However, you can connect your Xbox 360 to a PC, which lets you use your laptop screen as a monitor. This can come in handy when you want to play the 360 on the go but you don't have a television with you or if space is limited.
Purchase and install a video capture card on your laptop. Video capture cards are designed so users can input signals typically used for TV connections on their laptops; in this case, you'll connect your Xbox 360's video outputs to your computer.
Install any drivers that came with the video capture card. These drivers should be downloadable from the manufacturer's website and on an installation disc that came with the card.
Connect your Xbox 360 to the video capture card in the same way you would connect it to a TV or monitor. Connect the component or HD plugs to your Xbox 360, then connect the inputs to your video capture card.
Turn on your computer. Start the multimedia program used by your video capture card--likely Windows Media Player or QuickTime.
Turn on the Xbox 360. If connected properly, the Xbox 360's video output should appear on your laptop.
Computer monitors typically offer higher resolutions than large tube-based TVs. If you're having trouble reading text in your Xbox 360 games, reduce the resolution of your display in the Control Panel.