Ok, so the standard algorithms are:
1) Hamming distance
Only good for strings of the same length, but very efficient. Basically it simply counts the number of distinct characters. Not useful for fuzzy searching of natural language text.
2) Levenstein distance.
The Levenstein distance measures distance in terms of the number of “operations” required to transform one string to another. These operations include insertion, deletion and substition. The standard approach of calculating the Levenstein distance is to use dynamic programming.
3) Generalized Levenstein/(Damerau–Levenshtein distance)
This distance also takes into consideration transpositions of characters in a word, and is probably the edit distance most suited for fuzzy matching of manually-entered text. The algorithm to compute the distance is a bit more involved than the Levenstein distance (detecting transpositions is not easy). Most common implementations are a modification of the bitap algorithm (like grep).
In general you would probably want to consider an implementation of the third option implemented in some sort of nearest neighbour search based on a k-d tree