Through research family records. No, you don't trace surnames in genealogy. You trace your ancestors who just happened to have certain surnames. Surnames are not proof of country of origin or a relationship to another person. When surnames were taken in Europe the first part of the last millennium when they got through it was entirely possible that legitimate sons of the same man could have wound up with a different surname and still each one could have shared his surname with others with no known relationship. They weren't trying to identify men as a members of a families but needed to have a more efficient way of figuring who was who on records, frequently it was for taxation. They just had too many men with the same given name in the same town or village. So surnames do not have a family history. Your ancestors with the surname had the history.

Families frequently have information and it requires getting informaiton from them. it might be actual birth, marriage and death certificates, family bibles, letter from deceased relatives or ancestors, wills etc. That is how you should start. Good idea is to interview senior family members and tape them if they will let you. Oh, they will get into telling stories of days gone by you wouldn't write down but in those stories there likely will be clues that will help you break through a brick wall in your research. Good idea to go back on listen to the tapes again now and then as you probably will hear things you didn't hear the first time around. Some family stories are just stories and that's all but still there can be clues in them.

Then a person can go to a Family History Center at a Latter Day Saints (Mormon) Church where they have lots of records on people all over the world, not just Mormons. If a person finds some of their family in their database they can order microfilm of an original document to be viewed and printed. They have the microfilm readers at the FHC. They don't try and convert people. At least they never tried to convert me nor have I heard of them doing that to anyone else that uses their resources. A lot of their volunteers are not Mormon.

Check what your locall library has in genealogy.

You can use the web as a tool. There are lots of websites but look for those with records. Some only have family trees and I consider them a trash website. The trees in genealogy websites are submitted by the subscribers and there are errors. Once someone puts wrong information in their tree on a website, tons of other people will copy. The trees can be useful as clues. Two websites have both family trees and records. That is FamilySearch.org which is entirely free and the other is Ancestry.Com which many public libraries have a subscription you can use for free. Just be distrustful of family trees on their website or any website until you veirfy what they have with actual records. They both have U.S. censuses when they started in 1790. However it wasn't until 1850 that all family members were listed on the census. Before then they only showed the head of household.

A lot of people when they first start their genealogy make the mistake of trying to trace surnames in their family. Actually, you might not be related to a person with the same surname as you in the family line you got your surname from but might be related to that person in another family line.

It really depends on who is asking and why.

If you have an American passport, and go to South America to visit your grandparents, when you come back an official is going to ask for your passport. If he/she asks "Citizenship?" you'd say "American".

If a group of friends are discussing their heritage, and one says "I'm 1/4 each Albanian, Belgian, Cherokee and Danish - how about you?" you'd say half Peruvian (or whatever) and half American. If you do enough genealogy to know what heritages are floating around in your dad's gene pool, you can get more specific than "American".

The grammar Nazi on the next stool wants you to know that Jersey is a small island in the English Channel, and New Jersey is a state in the US of A.