This edition in "why has no one explained this to me before" brought to you from an email just sent to my friend with a new TV. Other editions have been dutifully tagged as directed - you can find them here.
So you've got a fancy new TV (or just realized you can do fun stuff with your old one). Mazel tov! But cable is lame and expensive so you want to get your content in other ways - whether it's abc.com or a collection of DVDs that has been collecting dust or files you've torrented or that touching slide show of pictures you put together for your grandparents' anniversary party. You've got two options (well, a lot of options, but two easy ones). Note: obviously this is how I do this but there are other ways — I'm updating the post accordingly with suggestions from the comments
You can (a) buy a separate machine (roku, playstation, xbox) or (b)connect your computer directly to the television.
(a) I'm down with the technology man, teach me how to stream my files!
Great. OK so if you have a device like the roku/xbox/PS/wii/apple TV (booooooo apple TV), it probably has things like netflix and amazon video and vudu installed on it already. The slightly more complicated (or rather, seems more complicated because no one told you how easy it is) thing is what to do with all of the pictures/music/videos that you have on your computer.* Everything needs to be on the same network for this — if you have a handy dandy VPN you're going to have to turn it off on your computer because they need to share an IP address.
If you have a play station, download the PS3 media server. Go into Navigation/Share settings in the app and in the bottom where it says "shared folders" just add wherever you have the files you want to watch. Then when you turn on the play station in the "video" section, your media server should pop up (if it doesn't, hit "search for media servers" and it should work). You can then either watch it from there directly or save the file to your play station (if it's something you'll watch repeatedly or you want to turn your computer off). Additionally if you go into the other play station sections (music, photos, etc) you can stream those kinds of files from your computer onto your television.
(shockwaver points out that universalmediaserver.com is the more uptodate version of this. I can't talk you through it because I use the PS3 one (and haven't had any issues with it) but you can check that one out too!)
(Gamecat235 points out that the PS3 media server also works on the XBox. I have no idea how to access it on said console but in terms of the computer end same steps will apply. Fluffybutt has talked through xbox stuff in the comments for us.)
If you have a roku, you're going to use plex. Download the plex media server on your computer and set it up. It's going to open up in whatever your default browser is.
Under "my library" you're going to add (the + sign) whatever folder has all of your stuff in it. Then on the roku you go into the plex app (which you downloaded) and it shows all your files. Handy dandy. It will play any kind of file (mkv, avi, mp4, etc).
I don't use XBox for moral reasons but I gather it runs plex as well. Don't get me started on Apple TV. You dug your own grave with that one.
If someone is more familiar with how to do it on other platforms let me know and I'll add it in. I've been a playstation person since Rayman.
(b) I don't want to buy something else/the concept of wireless streaming terrifies me/I want to watch something I can't stream on any of those platforms:
OK grandpa, settle down. This is easy, but requires you to sacrifice your computer while viewing.
If you are using a mac, your best bet is this. You plug it into the little hole on the side of your mac marked with a lightening bolt and plug the HDMI cable (kind of a flat/half hexagon shaped thing
into the other end. Then go to system preferences —> displays and click "detect displays." There's your television. OK great. Now you want sound I assume? System preferences —> sound —> output and choose the HDMI. Huzzah! Now your TV is basically a giant screen for your computer.
If you are using a PC there are a few options depending on your computer. Some have an HDMI port directly in there which simplifies matters greatly but there are also a bunch of other ports it could have.
. You need whatever the appropriate cord is. Go to control panel —> monitors. Under "display" you should be able to choose your PC and under "multiple displays" I recommend "duplicate" although you can choose to have it only displayed on your television. (Note — I haven't done external monitors on a PC for a while so that might be off on the new Windows).
The HDMI cable will carry sound but the others will not. To play the HDMI sound through your computer (thanks for pointing this out troughofluxury) you need to go to control panel —> audio devices and set your television as the output. If you are using the other wires, you can either use your laptop speakers or get one of these cables which plugs into your computer's headphone jack and uses the red and white (you recognize those, right?) wires to plug into the input section of your tv. Those cables are also handy if you ever want to connect your ipod to a stereotystem. Multi functional!
ETA2: lachategris wrote a great piece building on the above about using your computer as a cable box complete with DVR capabilities. You should definitely read it if you're looking to get out of dodge with the cable companies!
ETA: Another option, pointed out by xxiixi, is chromecast which you can buy from amazon and will allow you to stream from your desktop. I've heard good things but haven't used it myself so can't break it down
Note: The cheap $3 amazon HDMI cables are just as good as the $30 ones from Best Buy. NEVER BUY THINGS LIKE THAT FROM BEST BUY.
*Some of the devices have a USB port which is cool but may require formatting so YMMV