Worth noting that, while a *lot* of ZKP constructions that are used in the real world, use pairings, they're not necessary. If you even understand just the Schnorr signature (or more basically, the Schnorr identity protocol), you already know the basic ideas behind ZK proofs (see: "Extractor" and "Simulator"). A Schnorr signature (if it uses pubkey prefixing) is technically a "zero knowledge proof of knowledge" of the private key). For the general case of "proving a statement in zero knowledge" you need a more general construction, which you can get from the Schnorr construct using "generalized sigma protocols". And you can even construct properly general zero knowledge proofs by a clever extension of that basic idea, see "Bulletproofs"; this does not use pairings but only the same ECDLP assumption that Schnorr itself uses.

And there are other possibilities, see "STARKs" which are actually just succinct proofs, not zero knowledge proofs, but they can be extended in to zkSTARKs. These just use hashes, not pairings or elliptic curves even.