There are a couple of different types of blogs. You may want a journal format like this blog or a website type blog for a particular ancestor or ancestors (like the one I'm working on for my worst brick wall--Samuel Wilson). It's important to think through what objectives you have in mind for your blog. Do you want to get your family history out there in hopes of collaboration with someone? Are you envisioning a website that a group of people will work on?
A blog type website requires less technical knowledge. You won't need special software because it's available on-line and can be accessed from any computer. Multiple people can work on it at the same time because it's flexible and pretty easy for a beginner. A home page or front page will make the site look more like a website than a diary and gives you more control over the layout you want. Besides the blogger.com technologies, check out WordPress, Joomla! or Drupal or you could use a web-based genealogy program specifically designed to set up a website. I'm familiar with TNG (The Next Generation) but there are others. It's possible to keep your genealogy "in the cloud" to simplify collaboration, to work on it and have access to it wherever you are and to keep it always "backed up."
Questions can be answered by on-line help and by user forums. Our friends at Geneabloggers (the genealogy community's resource for blogging) remind us above of the fantastic resources they have made available. Be sure to suggest your blog for their blog roll to help your blog get better known and to garner suggestions from the experts there. I'm going now to get some information at their primer and resources sites for my new blog. See you there!