Your surname may have been created because of your ancestors occupation or a place where they lived. Perhaps you had a blacksmith in your family like the Smith family? Did your family live on a hill like the Hill family? Or your surname may have originated from the name of your father, John, the son of Edmund becomes John Edmundson.
Check out this free site to search for the meaning of your surname, http://www.ancestry.com/learn/facts. Keep in mind that you are not related to everyone who has your family name.
Remember that surname spelling could have changed over the years. Here is an example from my own family tree. The Jurxsce family immigrated to the new world in the 1700’s. Not sure what happened (probably a language barrier) but their name was changed to Yerxa. Both are pronounced the same way. Look for the variations and phonetic spellings of names.
Some researchers like using DNA to research their surname. Good choice for research if you want to know if a family with the same surname has a common ancestor or a way to locate your families geographical origin before you begin your research. (One myth about DNA testing is that it is the same as what is done for medical or criminal purposes).
Here is a good resource for researching your ancestors' surname from this Family Tree Magazine article written by Nancy Henderson. Check it out http://familytreemagazine.com/article/all-about-surnames.