Visit Tumblr's website. If there is a user logged in already, click on the computer power icon in the upper right corner of the screen. You should be directed to Tumblr's main page. Click on the "Sign Up" button on the far right.
Enter your email address, choose a password, and select a unique URL. Use a legitimate email address, as you will need it if you forget your password and to receive notifications and messages from other users. As for your username, choose something you like, since it will be part of your URL and visible by all. But don't worry--if you change your mind about your Tumblr handle, you can change it at any time under your blog settings.
Start posting! You'll need to pick out an avatar, a title, and a theme for your blog, but you're essentially all set. Go ahead and use Tumblr however you like; congratulations, you're officially part of the social blogging phenomenon!