First, the video connection. The easiest route will be to use your computer's HDMI, DVI, or VGA output. We recommend HDMI or DVI, since outdoor TV often accept higher resolutions over those connections than VGA. And although most TVs today don't have DVI inputs, you can still go that route if you use a DVI-to-HDMI adapter. (Since DVI doesn't carry audio, you'll still need to make a separate connection for sound see below.) If you opt for VGA, look for an input on the back of your TV labeled 'PC.' And if none of these options work with your setup, you can use your computer's VGA output and a VGA-to-component-video adapter to connect it to your TV.
Once you see your computer's display on your outdoor TV, you'll need to set it to the right resolution otherwise, you may see a pixilated or distorted picture. Be sure to use a resolution your TV is designed to handle (see the TV's owner's manual). If you don't see video displaying on your TV, there's a good chance you chose an incompatible resolution. You can tweak resolution settings by going into 'System Preferences,' and then the 'Displays Preferences' pane.
A note for folks using laptops: You'll need go into your computer's menus to 'extend' your desktop to a second monitor this will allow the computer to display video on your TV, as well as its own monitor. On Windows computers, you can access this menu by right-clicking the desktop, selecting 'Properties,' and then 'Settings.' Macs running Tiger, Leopard or Snow Leopard will auto-detect the new monitor and either 'mirror' or extend your desktop.
If you also want to send audio from your computer to your home theater receiver or TV, and you're not using HDMI, you'll need to make a second connection. Many computer sound cards today include optical or coaxial digital audio outputs that can connect to a receiver. If yours doesn't, you may want to consider upgrading your sound card. Or, you can simply use your computer's headphone output you'll need a mini plug-to-stereo RCA adapter to connect it to your TV or receiver.