There are several ways to install Wordpress and perhaps the simplest is to sign up for an account with wordpress.com. However that offers little in the way of flexibility. There are dozens of addons for Wordpress which add additional featureitis, but an account on wordpress.com doesn't allow you to install any of them. If you have some kind of hosting account it's relatively easy to install Wordpress on your own and add any addon you desire, however it requires more technical skill.
Installing Wordpress requires a web hosting account which provides PHP and MySQL support. There are several hundred companies providing this service.
Wordpress allows for multiple user accounts. This means a Wordpress installation can support multiple bloggers each with their own identity. People who are permitted to leave comments also register user accounts.
Wordpress sites are skinnable by installing themes. A theme is a combination of HTML and CSS which customizes the appearance of a Wordpress site.
Building a WordPress Blog People Want to Read covers all this and more. It is an easy to read book which covers all aspects of Wordpress installation, administration, and publishing content using Wordpress.