linear algebra – iteration procedure for least squares

Taking into account the classic problem $$min_x | Ax-b | _2$$, What would be the iteration procedure to solve this?

In my case, I am solving a least squares problem for GMRES:

$$min_x | H_n y- | b | e_1 | _2,$$

where $$H_n = Q_n R_n iff Q_nR_ny = b iff R_n y = Q ^ * b$$. So I'm solving for $$y$$ by replacing the back and then establishing $$x_n = Q ^ * y$$. Now, however, I do not understand what should be modified in the next iteration. I tried to configure $$b = y$$ in the next iteration, but that did not give a correct answer, even though the convergence occurred.

Can someone clarify?