In order to print the path you need to backtrack.

For example, suppose you are storing results of your subproblems in DP[i][j], what can done is to also store the decision that you made at that step in a separate matrix call it B[i][j].

In this case, DP[i][j]=min{DP[i-1][j]+1,DP[i][j-1]+1,DP[i-1][j-1] if s[i]=t[j], else DP[i-1][j-1]+1}

you can store in BP[i][j] the choice which gave you the min. For example if DP[i][j-1]+1, gave you the min. store (i,j-1) in BP[i][j] as a pair. So you know that at (i,j) you had chosen to delete a character and that before taking that decision you were at BP[i][j-1].

Now in order to print the path start with BP[m][n] and then backtrack using information you had stored in table BP[i][j].