In Order to jump start your genealogy search I will list a few places to start looking. 

Begin your search by gathering information readily available to you such as parents names, birth dates and places of birth and residence. Do this for each of your family members such as grand parents, great grand parents, and so on as far back as you can.

After you have this information assembled it is best to find a free genealogical software program to use (you may wish to purchase one at a later date).

After putting your information into your program so that it is organized begin your search.  There are many search engines available for you to use.  Simply type in the type of information you are looking for.  For instance if your grandmother knows that her parents married in a certain place but is unsure of the year search for marriage records for that particular place during the time her parents would have been old enough to marry.  Do the same thing with other records that might contain information you need.

I wish each of you good luck in finding your ancestors.  Happy Hunting!!!!