Your Tumblr dashboard is full of the most wonderful blogs, but only you can see that you're following them. If you want to give some publicity to your favorite blogs, you need to add a blogroll to your own blog. Exactly how you do this largely depends on your personal preference.
Adding a "Following" section to your blog will automatically list all blogs you follow. However, this only works for your primary blog. Open your blog's theme settings and look through them. If there's an option labeled "Show Following" or similar, toggle it on and save -- you're done. If the option isn't there, you can add an automatic blogroll to your theme yourself, provided you are familiar enough with HTML and with Tumblr's theme variables (see Resources) to figure out where it should go. Alternatively, simply switch to a theme that does include this option.
If the blog to which you want to add the blogroll is a side blog, or if you also want to include blogs that aren't hosted on Tumblr, you can set up a blogroll manually. An easy way to do this is to add the following code to the description section of your blog, replacing the placeholders with relevant information and adding more lines as necessary:
<a href="blog address 1">Blog title 1</a>
<a href="blog address 2">Blog title 2</a>
Alternatively, you can create a separate page for your blogroll. It'll be automatically linked from your blog's main page.