Jarkko Hietaniemi's String::Approx module is certainly your best bet to start with. In addition to the links provided by Roboticus, the following modules might provide some ideas of algorithms that could be used: Text::Metaphone and Text::Soundex.

Chapter 9 ("Strings") of Algorithms with Perl (Orwant, Hietaniemi, Macdonald) covers in some details some of the techniques that may be used. Otherwise, Simon Cozen's Advanced Perl Programming and John Orwant's Computer Science & Perl Programming both have a chapter briefly covering related techniques. (All three books are published by O'Reilly.)