There are very many blog providers, a large number of which are free. These can be found by typing "blog provider" into your search engine. Several free blogs are listed below. If you have any likes or dislikes regarding a particular blog service, you can leave comments at the bottom of the page.
The following video describes how to set up a blog in Google's Blogger:
There is also a site called EduBlogs which provides blogs specifically for educational uses. There is a free service, plus an advanced service for a very modest charge. A series of video tutorials can be found here.