You will need video editing software. I use Adobe Premiere however it is a commercial product and not cheap. There are some free or inexpensive options, neither of which do I know anything about. Editing the video is fairly simple and you can insert stills, music, transition effects (fades), etc.
Most digital cameras these days have a limited video mode. You copy the video from camera to PC and edit away.
Much like the old OFC picture gallery, sites like youtube.com, zippyvideos.com, etc allow you to upload and host your videos on the interweb.
Here's a video I put together a while back that should give ya an idea of what you can do.