If you wanna learn who your great great great grand parents were, I suspect DNA testing will not help you much. Actually most of the information for this you will get from church books, and official documents: Who maried whom, where and when. How were their parents called etc.
If you go back more than a few hundred years (eg 16th century in Europe) you will have to resort to less accurate documentation, as these things most likely won't exist anymore. however, they probably will still have kept tabs on who had to pay taxes and you will be able to follow your family name by who paid taxes when and for how many.
It's some serious work you would need to do (or someone would need to do), but can be very rewarding. My parents & grand parents have both been very interested in genealogy and have been able to retrace the family for the better part of 400 years. (and we moved within a 20mile radius over all these years.. quite amazing, isn't it?
If you "just" want to go back a few generations, it may be enough to talk to your family. Your parents will remember your grand parents and grand grand parents. Your grand parents even may remember the generation before that. They will also often know about your aunts and uncles twice removed. This kind of info is there, just rarely mentioned because it's assumed to be common knowledge.
Personally, I don't think, that using DNA testing to discover your ancestors is going to be very satisfying. At best they will be able to tell you with what likelihood you're related to someone else in their database... But your grand parents and grand grand parents probably never gave a DNA sample done, so they can not match your ancestry exactly.
They will probably tell you things like "There's a 12.42% chance that you are related to Charlemagne and probably general info such as you're 24.23% Asian, 40% Africane and 30% European. These kind of infos, which can of course be very interesting. (Given that my family moved within a 20 mile radius in the last 300 years, I'm fairly sure what kind of percentage I would get.