Is there an algorithm for normalizing data? I think I understand the process but how do I know when I have drilled down to the bottom?

don't believe there is any algorithm for it

you know you have drilled down when you can't have one column changing data based upon another column

ie - classic example
customer
city
state
zip

you could have a zip column with one city and state, then have another city and state with the same zip which would violate it

therefor you would need to create a separate table for holding zip, city, and state

once you have eliminated all occurrences that could happen like this, then normalization is done

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