Well it costs nothing but an internet connection and a device to surf the internet and than you have your fingers to create the blog.
Just make sure you have access to the internet and you are free to create a blog, there is no upfront cost for this.
Just open the Blogger.com or WordPress.com and signup for free with your email account which is also free.
You can also setup a custom domain which will cost $10 per year but its not important as you will get free sub-domain registered for you for lifetime.
Thanks for asking.