If the family/person you're looking for weren't in the same country as your search engine's default base try changing to the relevant country. I'm in the UK so default is google.co.uk - but if I wanted to look for someone in, say. Canada I could try Google's Canadian site (google.ca) and then restrict the results to Canadian sites - click on "search tools" and then "the web" and you get the choice of the web or "pages from Canada" - selecting the individual country still produces some oddities but does narrow the choices.
Another trick that sometimes gets better results, particularly for newspaper type announcements is to reverse the names - "Smith John" rather than "John Smith".
Becoming familiar with the full range of search techniques in a search engine and using those that are relevant can reduce results from tens of thousands to a more manageable number in many cases, though nothing is going to make it easy with some names!
