I want to use shear strength data of SS 304 for one application. How do we know how much strength any material possess in shear? How one can get the shear strength data of any material?
There are different test methods that you can use, they are available in ASME and ASM handbooks, for example ASTM B769 tends to obtain shear strength of aluminum alloys, ASTM F606 also obtains the shear strength of bolts and ASTM D732 shows the procedure of obtaining Shear strength of Plastics by Punch tool.As Sylvain told you can also obtain the tensile strength and use the von Mises or Tresca approximation to achieve the Shear strength.
Sylvain's answer already says it. Suppose SS 304 were isotropic, and you have the tensile yield stress from the data sheet, with no tension-compression asymmetry. Then the yield stress in pure shear using the von Mises criterion is sigma(shear)=sig(tensile) / sqrt(3).