How to prepare the silver atoms in Stern–Gerlach experiment with total angular momentum $j_z=+\frac{1}{2}\hbar,-\frac{1}{2}\hbar$? Total angular momentum at $z$ direction $j_z$ is summation of orbital angular momentum $l_z$ and spin angular momentum $s_z$ of many electrons in silver atom.
$j^2=j(j+1)$,$j_z=-j,-j+1,...,j-1,j$
The stream of silver atoms splitting in two direction means $j=\frac{1}{2},j_z=+\frac{1}{2}or-\frac{1}{2}$,my question is why the silver atoms always at this state where they always splitting in two streams in Stern-Gerlach experiment?
 A: The silver atoms are not "in this state".  The surprise of the Stern-Gerlach experiment is that, however you orient the magnetic field gradient, the beam always splits in two and only two components, and splits along the field gradient.
In other words, if you orient the gradient along $\boldsymbol{\hat x}$, the beam will split along $\boldsymbol{\hat x}$ so that one component has $j_x=+\frac{1}{2}\hbar$ and the other $j_x=-\frac{1}{2}\hbar$.   If you orient the gradient along $\boldsymbol{\hat n}$, the beam will split in two along $\pm \boldsymbol{\hat n}$ so that $\boldsymbol{\vec j}\cdot \boldsymbol{\hat n}=\pm \frac{1}{2}\hbar$.  This is just the experimental evidence.
The interpretation is that atoms do not come out of the oven with their spin in a specified direction (i.e. their spin is NOT along any particular but unknown direction $\boldsymbol{\hat n}$).  If it were, you could tinker with the orientation of the apparatus and eventually orient the field gradient parallel to this $\boldsymbol{\hat n}$ so that all atoms would be deflected in one and only one direction. This simply does not happen experimentally.
Instead, the interpretation is that the direction of the spin is determined  by the field gradient once the atoms interact with the magnetic field.
So, as a direct answer to your question, to prepare silver atoms in the $j_z=\pm \frac{1}{2}\hbar$ states, take a magnet with a well-defined field gradient, orient it along a direction which you call $\boldsymbol{\hat z}$, and pass your beam through it.  The output of this is what you're looking for, i.e. states "prepared" in either orientations of spin.
Note that this has been verified for other systems:

*

*The version with hydrogen was done by Phipps and Taylor (Phipps, T. E., and J. B. Taylor. "The magnetic moment of the hydrogen atom." Physical Review 29.2 (1927): 309.) The paper is available but behind a paywall.

*The version with polarized neutrons was done by Sherwood et al.
(Sherwood, J. E., T. E. Stephenson, and Seymour Bernstein. "Stern-Gerlach experiment on polarized neutrons." Physical Review 96.6 (1954): 1546.)  The paper is available but behind a paywall.

The literature on this experiment is rich and the topic is still active, as per this arXiv submission.
