Start with a square matrix (A)
Find an eigenvalue (lambda) by solving (det(A-lambda I)=0)
Form the matrix (A-lambda I)
Solve ((A-lambda I)mathbf{v}=0)
Find all nonzero vectors (mathbf{v}) that satisfy the equation
Any nonzero solution (mathbf{v}) is an eigenvector for (lambda)
Repeat for each eigenvalue
Optionally scale each eigenvector by any nonzero constant