How do we turn that into an actual search problem? Once we have TF-IDF, we have this measure of each word's relevancy to each document. What do we do with it? Well, one thing you could do is compute TF-IDF for every word that we encounter in the entire body of documents that we have, and then, let's say we want to search for a given term, a given word. Let's say we want to search for "what Wikipedia article in my set of Wikipedia articles is most relevant to Gettysburg?" I could sort all the documents by their TF-IDF score for Gettysburg, and just take the top results, and those are my search results for Gettysburg. That's it. Just take your search word, compute TF-IDF, take the top results. That's it.

Obviously, in the real world there's a lot more to search than that. Google has armies of people working on this problem and it's way more complicated in practice, but this will actually give you a working search engine algorithm that produces reasonable results. Let's go ahead and dive in and see how it all works.