How do doctors assess tissue perfusion in a patient in shock?

See below. The primary way to assess overall health (reflecting perfusion) would be to check the vital signs. A common way to assess peripheral perfusion is to check the color of the tissue under the fingernails after squeezing. Peripheral pulses help assess tissue perfusion. Usually the shock is treated first prior to performance of a scan such as a brain perfusion scan or myocardial perfusion scan.
Many methods... Depending on which tissue you are talking about, there are many ways. Brain perfusion is reflected in level of consciousness. Kidney perfusion is assessed by adequacy of urine production and laboratory tests. Perfusion of the extremities can be assessed by skin color and tone as well as radiologic tests and angiography and other laboratory tests.