The trick is not really posting it to the web, the trick is to display it on a web page.
My question for you, do you have any experience whatsoever in building websites? ANy experience with CSS or HTML? If no, skip to the last paragraph. In either case read the ENTIRE post.
Flash video playback works decently on most(But not all) systems. It will cover the majority of your intended audience most likely unless you are a specialist website. It does, however, require both a player(Usually a .swf file) and the file to be played(Usually a .flv file). There are free(As in beer, and probably speech as well) players out there, probably the most popular and famous is the JW flv player. A google search should turn up more than you need on it, as well as appropriate documentation to use it on a web page, assuming you have experience as asked above. flv typically isn't that great of quality however, and reencoding an already encoded movie, which is what it sounds like you have, will result in worse quality. The newer versions can do h.264 encoding however so that is an option for better quality, but will count out slightly more platforms to be played on, but will likely still cover the majority of your intended audience.
You can also directly upload those files, embed them in your webpage, and the people's computers that visit your site might try to play them with local software, say Quicktime player. This can be iffy though at times and depends on the codec support on the computer playing the file.
You can also just link to the file and have it download instead of embedding it.
Now all this aside, is there some reason you can't use a service like YouTube or Vimeo to upload and host your file, and you just link or embed it using the code they provide for doing this? These are free services, and will provide the Flash player and encode into flash for you as well, all you really need to do is copy and paste the code they provide for embedding the movie into your webpage. You could also altenatively just link to their website to play the file. If you have limited experience working with HTML/CSS, which not to be offensive, sounds like the case here, this is by far the best solution out there for you, much simpler and easier than dealing with providing a flash video player on your site along with the files, as well as being easier and probably, as much as I hate to say it, more dependable than embedding the video directly on your site.