I have an LG 47LM6200 HD 1080p 3d TV. I have an HTC3d phone. How do I get the videos to play on my TV?
As the LG 47LM6200 is DLNA compatible (Movie/Photo/Music), all you need for that is a DLNA server on your Android device. On my website you can find a list of apps for that: check with DLNA / uPnP Server and Clients. To make it easier for you, let me pick the most promising candidate:
BubbleUPnP is both, DLNA server and client – which means you can use it to "send and receive". For your case, you can pick local media from your Android device and stream it to your TV. Which can be done two ways even:
Variant 1: Use your TV to control
Start the app. Then check on your TV where the DLNA client is, have it look for available sources, pick your Android device from that list, and browse available media. It should allow you to access any movie, photo, or audio file to play.
Variant 2: Use your Android device to control
This will be the easier variant – at least easier to handle on "daily use". Switch on your TV, then again, start BubbleUPnP. It should allow you to pick a "media renderer" (first screenshot below: the first item in the menu on the left side) – your TV should appear in that list, pick it. Now browse your local media (same menu, two items further down), and select what you want to play. Once you've hit "play", the selected file should be streamed to your TV.
BubbleUPnP (source: Google Play; click images for larger variants)
This way you couldn't only stream your movies, but also music or your photos. The latter even as slideshow, if you like. And more: if you decide to buy the license, you could even stream stuff from the Internet; the free version of the app gives you the chance to try that first, but has a time limit on it.