Try viral marketing! Creating a buzz with unconventional tactics is the goal of most small start-up companies. Social media is an integral part in your marketing plan as well - more than half of the people in the world use some form of social media, so you can't afford to ignore it.
Most small businesses operate on a shoestring budget at first, but if you are creative enough you can come up with some fun and effective ideas to promote and market without spending a dime, or at least just a few dimes. Here are a few ways you can create buzz for your small business:
Those are a few ideas to get you started. Do a search for viral marketing and see what you come up with.