Where to start a deep web search is easy. You hit Google.com and when you brick wall it, you go to scholar.google.com which is the academic database of Google.

After you brick wall there, your true deep web search begins. You need to know something about your topic in order to choose the next tool. To be fair, some of these sites have improved their index-ability with Google and are now technically no longer Deep Web, rather kind-of-deep-web. However, there are only a few that have done so.