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You either list the elements, or you specify a rule fulfilled by all elements of the set (and only by them).
(1) List the elements, and (2) Define a rule that elements of the set must fulfill.
Let's say the set S has n elements. An element can be either in the subset or not in the subset. So There are two ways for one element. Therefore the number of subsets of a set of n elements is 2 multiplied n times which is 2^n
2x2^(n-2)
For example, if you take the set A = {1, 2}, then the following sets are all subsets of it: {}, {1}, {2}, {1, 2}. That is, all the sets that fulfill the condition that all of its elements are also elements of the set "A".