The special value method has wide application beyond combinatorial identities. In the context of combinatorial identities, it is most used with binomial expansion. For example, setting $a=b=1$ in the expanded form of $(a+b)^n$: $$(a+b)^n ={n\choose 0}a^n + {n\choose 1}a^{n-1}b+{n\choose 2}a^{n-2}b^2+\cdots+{n\choose n}b^n$$ immediately gives $$2^n={n\choose 0} + {n\choose 1}+{n\choose 2}+\cdots+{n\choose n}$$

Note: the special value method is a generally useful technique with wide application. The "more practice problems" link will include some non-combinatorial problems.