Following reblogs to their source is one way to find interesting content and new blogs to read on Tumblr, but it's not the only one -- you can also run searches. In most cases, Tumblr's inbuilt search function will serve your purposes perfectly fine; for more advanced searching, however, you may want to use a standalone search engine.
Searching on Tumblr
Tumblr's search feature only looks through three parts of each blog -- the title, the address and any tags applied to posts. Searches return both blogs and posts as the results. By default, the results include posts with your search terms anywhere in the tags -- for example, searching for "cute kitten" will return posts tagged "cute kitten," but also posts tagged "cute puppy" or "black kitten." If you want to search for a specific tag, prefix the words with a number sign -- for example, "#cute kitten" will only return posts with that tag.
Using a Search Engine
To search for words or phrases within posts, you need to use a standalone search engine such as Google, Yahoo or Bing. Add "site:tumblr.com" to each search to limit it to only Tumblr; if you want to search through a specific blog, use "site:blogname.tumblr.com" instead -- for example, you would type "site:staff.tumblr.com" to search only Tumblr's staff blog.