I think it depends on what you are wanting to giveaway. If you are crafty and are wanting to giveaway something that you have made then get involved in blogging parties such as the ones held by SITS (Secret is in the sauce) and 5 Minutes 4 Mom to build traffic for your contest, thus getting more traffic and hopefully more readers for your blog too. If you are wanting to do a sponsored giveaway from a company then you really need to build your readership or have a blog that is specialized to a particular topic.
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Toxic Free Blog - by Brittany Glynn
Brittany is a director of the Toxic Free Foundation and created the first ever Toxic Free Certification Program. Weekly, Brittany publishes the Toxic Free Blog and provides coaching to over 10,000 families in the United States alone. She is the author of a Toxic Free educational series and co-author of several Toxic Free learning programs. Brittany is also an award winning author.