A couple of ways will work depending on what you want.
First there is a device that you can add to your TV that will basically turn your tv into a large mirror of what goes on your cell phone's screen. Can't remember what it is but it's really just that, shows everything your phone shows. Requires a HDMI input on your TV to do so. This is a physical device that attached to it. Someone else might be able to tell you who makes it, there are a couple of them out there.
The easiest way is to use DLNA. Basically your tv either supports DLNA (Smart TV) or it doesn't. If your TV doesn't, then you can also add a blue ray player to your TV that does support DLNA (most of them on the market do). They also make a expensive dongle that will turn any tv into a DLNA tv but to be honest it's the same price as a full Smart blue ray player so the Blueray player is the better option.
When your TV or Blueray is DLNA capable you just need to make sure it is turned on in the tv or Blueray player and also that the option in your S3 is turned on (Settings/More Settings/Nearby Devices).
When it's turned on and you play a video, music file or show a photo on your S3 with either the Video player, Music player or Gallery, you can tell it to "Scan for nearby devices" (It's in the menu for each of those apps). It will find your TV or blue ray player and let you select it with this new icon that will appear when it sees nearby DLNA devices. The icon looks like a bunch of squiggly lines with a number on it representing how many devices it can see in the area. Once you choose which device to play it on it will play it on your tv.
The only disadvantage to this is only those apps will display to the tv until the other app makers add that ability.