There are four main ways to find relevant and reliable web sites which may contain information useful for your project.
There is a very important difference between the first three ways and the last one. Web indexes and directories, library web site subject pages, and faculty web sites all attempt to evaluate (at least to some degree) the web sites they link to and to provide some level of organization. Search engines simply retrieve whatever is out there that matches your terms - the good, the bad, and the ugly - all in the same pot!