1. Similar matrices

Given two matrices A and B that are similar, what is the procedure for finding the change of basis matrix, S with

$\displaystyle A=SBS^{-1}$

2. If $\displaystyle A,B\in \mathbb{K}^{n\times n}$ are similar matrices, there is a method for finding $\displaystyle S$ in a finite number of elemental transformations using the concept of equivalence of $\displaystyle \lambda$ matrices.
Another way is to use the fact that $\displaystyle A,B$ have the same Jordan canonical form, etc. All of this would depend on your previous theoretical knowledge.