A common saying around various help forums is this: "Google is your friend"--as indeed it is. I am continually astonished by what you can find out with a simple Google search. But the more you know about using Google, the better the results you will get. For instance, if I simply type:
Francine Schwieder
into a Google search box I get 12 pages of results! Outstanding, right? Well, not really. Even with two unusual names there are an awful lot of pages that are perfectly irrelevant, because they contain both names, but they aren't in any relationship to each other. Thus while the first two pages have results that are related to me, by page 3 the search results include pages that have nothing whatsoever to do with me. For example, the first irrelevant result is an Ophthalmology page with Medline search results listing articles by various researchers, one article having an M. Schwieder as an author and another with a Francine Grodstein as a co-author. Not very helpful!
One thing you can do to narrow your results is surround your search term with quotes. Thus this query:
"Francine Schwieder"
returns a mere three pages of results, but every single item found is either by me or mentions me.
Another thing you can do to get better results is add some search terms. Thus if I do a search on the name:
William Stinnett
I get 10 pages of results, including lots of contemporary items, such as a listing of current lawyers, one of whom is named John William Stinnett. What I want is something about an early ancestor. If I include a name involving some other ancestor in the same line I am more likely to get genealogy results. Thus, since I know he is an ancestor of my great grandmother Rosa Hollingsworth, I'll try this search:
William Stinnett Hollingsworth
Bingo! I now have links to a whole lot of genealogy sites. If you find a good site you can have Google search just that site. What you need is the URL, excluding the first part and the specific last part. Thus if I click on one of the links I find with the above search it takes me to this very specific page:

The page turns out to be very useful. But suppose I want to find something slightly different and decide this is a good site to look for things? I could, of course, try the address of http://genforum.genealogy.com/ and assume it will have appropriate search tools. Or I could simply amend my original Google search by adding another search term and a site restriction, thusly:
Stinnett Hollingsworth Isham site:genforum.genealogy.com
Once you've found a good site you will discover it often has useful links to other web resources that can help you gather more information. Unfortunately you will also discover that many of the places require a fee to use their services. There is one for instance that thinks paying 30 bucks a month is perfectly reasonable. Maybe it is. But you can find a whole lot of information without shelling out any money at all.
Well, that's what Stewart Brand said at the first Hacker's Conference in 1984, and there are a lot of people who agree. Especially anarchists and the stereotypical nerd living in his parents' basement. Whether information wants to be free or not is an interesting philosophical debate, but in practical terms there is a lot of it that is free, and with a bit of digging you can find it.
Indeed, there is one category of information which is free, in that you can use it easily without paying anything. In another sense it isn't really free, but you have already paid for it. I'm referring to the mountains of data acquired by various government agencies and financed by tax dollars. You can often visit a government web site and get useful information there. For instance, my immediate ancestors came from Illinois, and the state maintains an online Archive with all sorts of treasures, free for everyone to use. And it isn't just Federal or State govenments that have web sites these days, so do counties and cities, which is one reason why it is important to know not just when, but also where someone was born.
One piece of information I had always known is that my father's people lived in Palmyra. I had even been there and visited my great aunts on several occasions when I was young. Looking up Palmyra I discovered it is in Macoupin County. And Macoupin County has a web site. Their web site turned out to have little of interest, but in Googling it to get the URL I found something else that was immensely helpful: a Macoupin County genealogy site. Among the many treasures to be found there were the census records for 1830 thru 1860. Using them I was finally able to trace the Chisms back to 1800, in Virginia, and the Meyer line back to an immigrant from Prussia.
While you are investigating resources available for a county where your ancestors lived, be sure to check to see if there is a list of cemeteries for the county, there often is. Furthermore, sometimes there are lists of graves and even pictures of individual grave markers online. I remembered my father taking me to an old family cemetery out in the country once, and that he mentioned another family cemetery as well. When he himself was buried, it was next to the grave of his grandmother in one of the main cemeteries for Palmyra. I was surprised to discover that cemeteries in Macoupin county, including not only the larger ones, but several of the smaller family ones, had been visited and had their grave markers copied or photographed and posted online. One example, from the RootsWeb site, is this page:
Not only are there photos of the cemetery, there are additional photos of individual markers, as well as a written list with transcriptions of the legible information on the markers, in alphabetical order. Often the information on the markers can give you exact birth and death dates, and might even help in sorting out relationships, and you may discover the names of other possible relatives and ancestors.