You can create a free blog on wordpress.com but you'll be limited to what you can do.
I recommend just saving the money and getting a web hosting account and install wordpress blog script on a paid web host where you have full control over it.
And get a domain for less than a $1.00 a month.
If you want to earn money with your blog or website in the future than paying some money now will pay off in the long run.
Your blog and website will be seen as more professional and have a higher chance of ranking in googles search results.