For a public one-way function $f()$, we can use zero proof to prove I know some secret $x$, such that the output of $x$ is a specific number $y$.
However, in zcash, I need to prove that I have some secret $x$, then $cm$ which is the commitment result of $x$ is a leaf in Merkle tree. Here, $cm$ is not a specific number and it is secret.
How should I prove this statement? I cannot figure out the circuit structure and the process using ZK-snark.
"[T]he process using ZK-snark" is to express the statement being proved as an R1CS system, produce proving and verifying public keys, produce and verify a snark-proof. A large non-trivial R1CS system is often expressed in terms of "gadgets" according to high-level "circuit structure".
A popular algorithm/proof was introduced at https://eprint.iacr.org/2016/260.pdf and implemented in libsnark. Zcash-specific "circuit" is documented in their "protocol" paper.
