Welcome to (hopefully) one of the most comprehensive one-stop-shops for Zero-Knowledge beginners. Having recently graduated college with a degree in Computer Science, I can relate with the people who think they don't know enough Math or Cryptography to get on the ZK track. But having gone down this rabbit hole for a month, I can promise you don't need to be an Alan Turing to understand the most of what's going on here.
This tutorial is mostly meant for an undergrad-level builder-focused crowd that is looking for a quick and dirty way to get their feet wet and create a more scalable and privacy-preserving version of web3.
I wrote a few google docs to help you understand the very basic premise of what we are trying to accomplish with Zero Knowledge Proofs. Based on what you feel comfortable with, I recommend giving both of these a pass -
Once through this, I suggest (mostly since I think STARKS >>>> anything else in the world) that you familarise yourself with the math behind StarkWare. This might come in handy since we will be focussing on StarkWare going forward.
If you are a developer, and want an absolutely bare bones example of an implementation, check out the repository folders above.
The first one is a solution set to Cairo Playground - an initiative by StarkWare to help on board developers to their ecosystem. The second one, though, is a DIY ERC-20 implementation with testing, JS integrations and lots of links to resources and cool new projects you can try out for yourself !!
Once you are feeling good about the general structure of this code, and want to build something from scratch, I recommend using this template for Protostar.
I believe the best way to learn something is by doing it. I highly recommend you read the following 2 case studies on existing ZK-based offerings in the web3 market. Both of them, ZCash and StarkNet, have carved a niche for themselves and proven to be robust solutions.
Once you are done here, I urge you take a look at this mental model of the ZK Industry as it exists today. If you are looking to understand how ZKPs fit into the bigger picture of web3, I also recommend reading about fractal scaling. Finally, do read this interesting paper by the Wharton School on ZKs for a more business oriented perspective.
Finally, I think it's important to acknowledge that in such a fast growing space - you can never know enough. The best ways to stay in touch, IMHO ...
Follow people like Thor Kamphefner, Eli BenSasson, Vitalik Buterin (Duh !!), Uri Kolodny to get the latest and greatest.
Checkout more projects like Only Dust , NetherMind, StarkWare, Arbitrum, Extropy and play some Dark Forest.
Finally, keep reading and keep learning. There are many more elaborate resources that you should probably upgrade to once we are done here - like The ZK Podcast, the Delendum Reading List and Encode Club's ZK Hackathons and training series.