How do you determine the amount of vitamin c present in a fruit juice sample?

Well, the simple answer is to find out what percentage of real juice is in the juice you have, then if the manufacturer fortified it with more Vit C.

If you're talking about lab tests, I have no clue.

You can look it up in nutrition tables.

For example: Nutrition Fact Sheet: Vitamin C, Nutrition, Feinberg School of Medicine

This isn't very comprehensive, but you get the idea.
Google "nutrition tables" or "vitamin C content".

Did you want a method?

You can look in Food Analysis Laboratory Manual by S. Suzanne Nielsen (available for free @ books.google.com) for the “official method” for measuring vit C in fruit juices (p47).