Many companies provide free web hosting for simple web sites. You
will need to spend time researching free web hosts. You will need to
look at the services offered by each host for free to determine if they
are truly free for you.
You will find that free web hosting companies often offer limited support and only basic services for free. They will often tack on fees for non-basic services. Many times they will also dynamically insert advertising on your site (kind of defeats the purpose of you having your own advertising on your site).
A great place to search for a free web hosting company is at a community that specializes in free hosting. Users on these communities will often offer reviews and comments on specific free web hosts. Read a cross section of reviews, and post your own questions.
Some possible communities to research include:
FreeWebSpace.net
Hostsearch.com
Devshed Free Hosting Forum
GIDForums