How do many public keys correspond to one private key?
The answer is in Hierarchical Deterministic (HD) wallets. These create a tree-like repeatable sequence of key pairs (private and public) from a master private key.
Each public key is associated with one private key.
See BIP-32
Standard ways of spending Bitcoin involve reference to an output of a previous transaction and hence to a previously used public key. It typically needs the corresponding private key to be used to generate a number that will satisfy the spending script.