how do I play live movies from my computer on my smart tv

Depends on the system you have - no one can assist without knowing that.

You can connect the computer to the TV by a VGA or HDMI cable. Or you can obtain a wireless TV dongle such as Google Chromecast which uses your wi-fi. If you are using Win 8, then you can also use Miracast with a wireless Microsoft dongle. Miracast is a direct wireless connection and does not need wi-fi. Roku devices can also do this, but applications are limited.