To start a blog, we need to have blog software for it. There are several blog software available for selections nowadays. The most popular one is blogspot and wordpress. Both are free to use.
Here I recommand you to use blogspot if you want to make money via blog; if you want to blog for your own pleasure, you can choose wordpress and blogspot, it doesn't matter.
I'm not Google supporter here. I recommand to use blogspot, because it has wide selection of templates, and the most important is that it allow you to put in any scripts for free. Unlike wordpress, it doesn't allow any scripts. Why scripts are important? Because most of the advertistment companies want you to put/install a script on your blog, so that they can trace and show the adverts.
Own domain or Free
In the beginning, it is not very important whether you have your own domain or free hosted. But if you want to earn more through your blog, it is better to have your own domain hosted. More and more publishers require you to have own domain, or else they wouldn't let you to earn from them. So, I strongly recommand you to have your very own domain hosted, if you want to put your efforts in blogging for money.
If you have any questions regarding these topic, feel free to drop a dollar(comment), I will answer you back asap.