Connect a Macbook to a TV Using HDMI

Step 1:

Check Macbook Version

First off, you'll need to make sure you have the correct version running on your Macbook. To figure this out, you'll need to:

Go to "About This Mac" in your Apple menu (under the Apple icon in the upper left-hand corner)
Then, double-click the version text (for example "Version 10.8")
Type the serial number into the Apple Support Page. You'll then see what version you are running on your Macbook.

Step 2:

Finding the Right Mini DisplayPort to HDMI Adapter

In order to fully support both audio and video transmission, the Mini DisplayPort to HDMI Adapter should support the VESA-1.1a DisplayPort Standard. Apple recommends the following three adapters which are known to adhere to this standard:
Moshi Mini DP to HDMI Adapter with Audio Support
Griffin Mini DisplayPort to HDMI and DVI Converter
iWires Mini DisplayPort to HDMI Adapter

Step 3:

Enable Audio-Output Over HDMI on Your Mac

Open System Preferences
Go to Sound Settings
Switch to the tab “Output”
If you have connected the Macbook to the TV as described above, you should now see the TV displaying your Macbook screen. Now, select the TV and you're all set.

Trouble Shooting:

I have set up the connection as described above, but the TV is only showing the Macbook desktop wallpaper

Usually you'll have to drag the video window that you want to appear on the TV screen right outside of the Macbook screen to make it appear on the TV. Alternatively, you could go to Preferences --> Displays and click on "Detect Displays." Choose the "mirroring" option and your computer screen should now be displayed on your TV 1:1

The TV is not showing the Macbook video signal

Try switching through the different HDMI input channels of your TV. Most TVs should automatically detect the Macbook video connections, but some models will require you to select the video input manually.

I have a new Macbook model with Snow Leopard installed but the Audio Output over HDMI is not working

Make sure your system has the latest software updates installed. With the upgrade to OSX Snow Leopard there was a Mini Display Port Audio Output bug, see this discussion in the Apple support forums.