Set the TV to the input you connected the HDMI cable to.
On your computer, if you open the Displays preferences and do not see an Arrangement tab (or there is an Arrangement tab that shows only a single monitor) then there is something physically wrong with your connection. Try clicking Detect Displays just to see if the computer can now sense the presence of the connection. Check your cables and make sure the mini-displayport plug is pushed firmly in. Mini-displayport (in this case same as thunderbolt plugs) plugs can be a little tricky in that you need to make sure the plug is fully seated in their socket.
If you do have an Arrangement tab, and it shows two screens, then click Gather Windows to bring the TV's Displays preferences on to your main screen if the TV is not yet showing an image. Set the proper resolution (probably 720p, 1080i, or 1080p). Set the refresh rate (probably 60Hz) if that preference is shown. You should see a picture at this point. I recommend turning off mirrored displays if it is enabled.
You may have to play with the underscan/overscan settings on your TV and the displays prefs for the TV if the picture is too small or larger for the TV screen.
Also, you need to set your Sound preferences to output to the HDMI connection.
And if running Lion, do not run in Lion full screen mode.
