Searching for ancestors online can be daunting because much of the information you seek is behind pay walls. There are some free places you can search for items though.
One of the first things you should do is make a list of the the names you know - both maternal and paternal grandparents are a good start. Then see if they can tell you the names of their parents - your great grandparents. Keep in mind that maiden names can be important when you are looking into branches of your family tree. You could also choose the one branch - that of your last name.