Method 1: Pay someone to host your website. You'll have to upload your movie files to their server. Costs range greatly depending on the access you want, size of storage, and frills. Another factor is how much downloading you're going to get. For instance.. if the movies are only a few meg in size and only a few people are downloading then you'll be fine, but if you have large movies and everyone and their uncle are downloading then you'll be asked to increase your bandwidth (increasing your cost).
Method 2: Have a spare computer with something like XP or Win 2000. Turn on the IIS fuctions (you'll have to do some reading up on this). Create your website and connect it to the 'net. Friends/family can connect to your system by typing in the IP address of that computer. This method is nice since you're not renting space and you have direct access to when the info is available. One issue you may have is ensuring it's up whenever you want, hosting companies will have backup systems in place to ensure your data is always available. Bandwidth is limited to your ISP.