Although many people also use them for rambling and commentary, tags are the way you find posts about things you love. Whether you need to know the exact tag that was used on the post, though, depends on whether you're searching Tumblr as a whole or looking through a specific blog.
Tumblr as a Whole
Start typing in the search field at the top of your dashboard and Tumblr will immediately display both tags and blog titles matching your search. Click on a tag in the search results to show a page listing popular posts with that tag. Also on that page is a link to show recent posts with it, as well as a link to add the tag to your tracked tags. Click a tag on any post on your dashboard, and you'll jump straight to a list of recent posts in it; from there, you can also track the tag.
Click a tag on a blog's main page or an individual post page to see all posts on that blog with that particular tag. You can also do this by adding "tagged/yourtag" (without quotes) to that blog's address, replacing "yourtag" with the tag you're looking for, but with pluses instead of spaces. For example, to get all posts tagged "Tumblr Tuesday" on the Tumblr staff blog, you'd enter "http://staff.tumblr.com/tagged/Tumblr+Tuesday" in your browser's address bar.