When you first sign up for Tumblr, it will assign your blog a URL based on the user name you entered to create the account. But you'll probably want to customize the name so that it's related to what you'll be blogging about, or so that it's a bit snazzy. No problem. To create a new name, go to your Dashboard, then click on the title you gave your blog. Next, click Blog Settings (in the sidebar on the right) and enter the URL you'd prefer in the URL box. You can also add your photo here; square photos that are 128 by 128 pixels or larger are best. Click Save (bottom left) and you're done.
Now for the visual elements. Scroll to the bottom of the page, where you'll see the Tumblr copyright and a line of small, white words. Click on Themes to pull up a page full of themes, both plain and fancy, free and for purchase. Select Free themes on the left (or whichever type you want), then click on one you find appealing. You can hit a button to preview the design, then install it if you wish, or browse around some more. You can change themes after you've installed one, but you won't be able to preview it beforehand.