Geochemistry Question:

Various ways and techniques can be used. With many mountains, the rock in the mountain can be sampled and then a dating technique applied to find the age.
For instance, radiometric dating may be used to find the age of the rock. These techniques exploit the half-life of naturally occurring radioactive isotopes of elements present in tiny quantities to help work out how old something is.
With some mountains other techniques may be used, for instance at a plate boundary scientists may be able to wind back time to work out when the plates must have collided and formed mountain ranges such as the Himalayas.