What is the best way to market a new online business for the least amount of money?

[M P]

try dmoz.org; blogs on the same type of product/service; you can exchange links with others businesses(not competitors)but those with the same type of customers; you can do a blog on a site that would have customers interested in that.
If you exchange links then make sure those sites have at least a 50% page rank - you can get a page rank from Google toolbar.
Put your keywords into the search and see what types of companies come up then you know who your competition is, but you may find similar businesses you can link with.
Search for directories for that type of biz and get listed in those. Put promote a biz in your search and check some of those out.
Good Luck