Hi Buckleysmom,
When I first got into geneology I did some research into free software and managed to find a program called Personal Ancestral File (PAF). This was developed by the The Church of Jesus Christ of Latter-day Saints (aka the Mormons).
Mormons have a connection to ancestry as they perform ceremonies that I like to call "retrospective baptism", hence their interest in such software.
The program itself is "no frills", but it does most of what you'd ask of such a program and is very easy to use. Importantly, it uses the GEDCOM file format, which is the standard data interchange format used by genealogy software in general. If you decide to get a better program later you'll be able to carry your data across.
You can find it by following this link:
http://www.familysearch.org/eng/default.asp?page=home/welcome/simplePAFRegistration.asp
They require a simple email registration before you can download, but in my experience it is nothing onorous.
You can also get PAF Companion, which allows you to "Print your family tree in colorful ancestor and descendant charts. PAF Companion is easy and fully compatible with PAF."
Please note that the http://www.familysearch.org website itself is a useful resource for doing family searches.
Good luck, regards,
SB