If you know absolutely nothing about HTML or anything else, then that's what you want to start learning. check out
http://www.w3schools.com for great guides and tutorials. Start with HTML and CSS.
You can use software, but it's usually not as useful if you don't know anything about websites yet. If you want to try one, go download the open source web editor, NVU at
http://www.nvu.com
You probably don't want to try to serve the site from your house. Web servers are usually kept at data centers with consistent upstream speed and bandwidth. You can download at 1mb at your house, but I would guess that you can only upload at like 256mb/s or something like that. It would not be very fast or reliable, and if you intend to serve videos it would definitely not be the best option.
Another question would be about the videos; what format are they in? what resolution? about how big are they? if you just want to send your friends videos you could use one of the many file uploading sites. My current favorite is
http://www.gigasize.com
To have your own website, you don't have to host it from your home. You can get the same lack of restrictions on the type/size of video and stuff that you upload, and you'd get better bandwidth if you get some space on a web server.
If you want to play around with it first, you can check out some of the free servers available, though there may be ads or other restrictions it would help you get an idea of what it's like. Check out
http://www.free-webhosts.com to find one to try out. I'd say to look for one with FTP access and php support.
You can also buy a domain and get some web space to call your own. Some popular web hosts include
LunarPages and
BlueHost