1) Set n to be the length of s. Set m to be the length of t. If n = 0, return m and exit. If m = 0, return n and exit. Construct a matrix containing 0..m rows and 0..n columns.
2) Initialize the first row to 0..n. Initialize the first column to 0..m.
3) Examine each character of s (i from 1 to n).
4) Examine each character of t (j from 1 to m).
5) If s[i] equals t[j], the cost is 0. If s[i] doesn't equal t[j], the cost is 1.
6) Set cell d[i,j] of the matrix equal to the minimum of: a. The cell immediately above plus 1: d[i-1,j] + 1. b. The cell immediately to the left plus 1: d[i,j-1] + 1. c. The cell diagonally above and to the left plus the cost: d[i-1,j-1] + cost.
7) After the iteration steps (3, 4, 5, 6) are complete, the distance is found in cell d[n,m].