To begin, go to the wordpress homepage at www.wordpress.com and click the orange (used to be blue) “get started” button.
On the account creation page you will give them an email address to associate with your account and choose a username. Your username will become part of your URL as well. For example, my username is “the21stcenturyteacher” and my site’s URL is “the21stcenturyteacher.wordpress.com”. It’s best to pick a username that has some relevancy to the topic of your blog though that isn’t a hard rule. Choose a password and then create your blog. The free blog is all you need for now. You could upgrade to a paid version if you found the added features valuable to you.