How can I advertise my home business for free?

[Richard]

The best possible options for you, considering the lack of details on your question, are social media marketing, SEO, and blogging. Setup you blog and complete all your social profiles. Connect, share, interact, and contribute while making your business a part of the solution or needs. Then drive traffic through SEO.. you can use:
Directory submission, search engine submission, article directories, blog commenting, guest blogging, blog directory submission, press releases, content sharing, forum posting and participation, profile linking, wikis and q&a sites, rss, link baiting, video & image distribution and marketing, manual link sources search (authority/edu/gov), reverse engineering, social media/web 2.0, other techniques based on latest trends

Drive traffic through PPC ( not Google Adwords at this point.. For instance, Facebook Pay per Click can be a lot cheaper)

Seems like a lot of work... But most of these can be done for free or at lesser cost.