Google is the most powerful web search engines ever created. It has come into the lexicon as a adjective, "just Google it". And best of all it is free for all genealogy researchers. For someone who has little experience doing Internet searches a Google could lead to few results. But by learning a few simple search techniques, the better your results might be.
The more uncommon the name the better. So searching for John Smith will be next to impossible so you may have to go in a different direction such as John's father, children or siblings. If John has a brother named Mortimer finding Mortimer the correct Smith family will be much easier when looking for Mortimer than solely by searching for John. You may need to come in backwards rather than starting with who you are looking for
One time a friend and I were both researching our family tree. I told him I was stuck on Henry Lewis and couldn't get past him in Wales. He said, " I have Henry Lewis in Wales too and I have three generations past him as well." For two days we thought we might even be related through old Henry. That was until we get our books out. My Henry Lewis was 1792 and his was 1850 and none of his ancestors had any names in common with mine and none of my descendants fit his chart. So our brief time as relatives ended. When searching Google add as much information as you can about dates and try different dates such as birth marriage and death. All dates are important because you never know if someone is researching your relatives spouses family and only has a marriage date.
Location, location, location
Tracking down someone to a county or town can help with finding the person in a Google search. This is may or may not help. In my own research I tracked my ancestor with and uncommon name of Manus Boyle to the town of Hazleton Pennsylvania in 1880. But upon further research apparently Hazleton was a popular town for the Irish as there were 6 families named Boyle there in 1880 and two of them had a patriarch named Manus. So even when I thought I found him I had not. I had to delve deeper and compare to other information I already had to know I had the right guy.
So when Google searching knowing the location and adding it to the search can be helpful, but also be mindful of the area as well. I was doing a search of a local newspaper for a relative and found a great story about his weeding and the guest that were there in the society section. But the section was for the next town over, because that it the town where the church was located. If I had limited my self to the town he lived in without expanding to the nearby area I would have missed the story.
Also finding your relative based on events that might have been involved with such as a war. Searching for there name followed by the war of a particular battle may provide you a website that list more information about them or the battle that they were involved. My paternal grandfather was a bombardier in WWII and died when my father was young. But through Google I was able to find a website about his unit which list every mission that he went on and what the target was.
Rank or title
Any title that your relative had will help your Google search for them. Identifying them as doctor or Captain will help narrow down to the person you wan to find. So if they had a title try search for them using that title.
Search what you want
Adding what you are looking for could also narrow the results. Adding the term "obituary" should in theory remove all living people from your search results.
All of the above
Using Google for genealogy is still a lesser source as it deals with mostly current events and people but if you have time or at a dead end it may be worth your time to spend a few hours seeing if you can get information you do not have. But doing it the right was will lead to more fruitful results.
Examples from most general to most specific:
Name search: John Smith
Uncommon name: Mortimer Smith
With date: Mortimer Smith 1863
With location: Mortimer Smith 1863 Spotsylvania Virginia
With event : Mortimer Smith 1863 Battle of Chancellorsville
With title: Major General Mortimer Smith 1863 Battle of Chancellorsville
With what you want: Obituary of Mortimer Smith 1884 near Richmond Virginia
This should help get started with what to search, in a future post I will discuss other syntax options within Google to get even more out of your Google search and narrow down your results.