The article has good tips, but Unicode normalization is just the tip of the iceberg. It is almost always impossible to do what your users expect without locale information (different languages and locales sort and compare the same graphemes differently). "What do we mean when we say two strings are equal" can be a surprisingly difficult question to answer. It's practical too, not philosophical.

By the way, try looking up the standardized Unicode casefolding algorithm sometime, it is a thing to behold.