This may start to sound like a broken record, but it really is a great idea to post your family file online somewhere. There are so many free sites, and it is so easy to do! The first thing you need to do is have your information stored conveniently in any number of genealogy programs for your computer. Personally, I prefer Legacy, but PAF is the simplest, and its a free download from www.familysearch.org.
Once you have your names and dates entered, export it to a .gedcom using the program's "export" function. Be sure to include sources, but exclude notes and information for living individuals -- usually just a matter of checking a box on the export screen.
Then find the site you want to post to. Rootsweb.com shares their pedigree charts with Ancestry.com, but is entirely free for anyone to peruse. If you want your OWN website where you can also post pictures, etc, I recommend www.familytreeguide.com. There are other sites, including www.tribalpages.com and www.geni.com that work great too. Sign in for your free account, be sure to record your username and password, and then upload your gedcom. Don't wait until your file is "finished" or perfect, because I can guarantee you, you will be long dead before that ever happens!
The next thing you know you'll be meeting new "cousins" from all over the world if you're lucky! The worst that will happen is nothing at all. The best is that someone will contact you and share long-lost information from their family bible or attic!