TV Options
The first thing you should always check is your TV itself so you know it's set up properly to receive your PS3's signal. Nearly every TV has multiple connections, and unless you tell the TV which connection it's supposed to use, it may try to display an image from the wrong one. You can normally cycle through every connection for your TV by pressing a button on your remote, usually labeled "source," "input" or "TV/video." That tells your TV to try to accept the picture and audio from a different set of connections. If you look at the jacks that PS3 cords are plugged into on your TV, you'll find the label for that connection; that's the input your TV needs to use. If you work through all of the connections and the TV doesn't display anything from your PS3, then you need to check on the connections and the PS3 itself.
Connections
If any of the cord connections are loose between the PS3 and your TV, the audio or video may be distorted or may not be present at all. You should check the connection on the back of the PS3 and make sure the cord or cords are securely plugged in. Then make sure that the cords are also securely inserted into the jacks on the TV. Lastly, make sure the cord isn't damaged in some way. If the cord is frayed or cut, you may need to replace it before you can continue using your PS3. If the TV and the cords are set up and working correctly, then the problem is usually with the PS3's settings.
Video Reset
Your PS3 may be sending an unusable signal to your TV, such as a high-definition image to a connector that only supports standard definition. If you reset your PS3's video output, it will send a standard picture signal that is low resolution and any TV will accept. First turn off your PS3 if it's on; just hold the power button for a couple of seconds until you hear the console beep and see the LED turn red. Now press and hold the power button. You'll hear one beep right away, but you should continue pressing the button until you hear a second beep, then let go. This resets your PS3's video output.
Picture Setup
Once you've reset the picture, you should configure it again so that you're viewing the best image possible on your TV. Go to the "Settings" portion of the XMB menu and select "Display Settings," then "Video Output Settings." As you work through this process, you'll advance to the next step on the screen by pressing the controller's right directional button. First select the connection you are using on your PS3. If you're not sure, look at your TV and see which jack you're using. You should select "HDMI" if you're using an HDMI port on your TV; you should select "Component/D-Terminal" if you're using component ports; you should select "Composite/S Video" if you're using a composite (or RCA) port or an S-video port. Often you'll have to select the resolution options that your TV is compatible with next. You should check every resolution that your TV can accept. If you don't know, check the TV's documentation or just work through the list, checking each option and then advancing. If the screen goes black and you can't see anything, then you passed the TV's maximum resolution, and in a moment the PS3 will revert to its last usable settings and you can finish the setup.