You can do a mtDNA test on your self, which will provide a profile for you, your mother, your mothers' mother, ... This will give you your maternal grandmother's Haplogroup and mtDNA profile.
If you are a male, you can also have a yDNA test done on the same sample - either by initially buying a combo test, or by ordering an upgrade. If you are female, you'll need to test a male family member to get your surname yDNA profile
This series will give you a lot of specific info:http://www.worldfamilies.net/smart