I have put together a comprehensive Tutorial to help anyone learn to Mine Zcash. Since Zcash is only Linux based many people on Reddit and the Zcash forums have been discouraged from getting involved because it can be a steep learning curve.
I hope that someone who has never used Linux before will find this guide and be able to set up their own machine with their existing hardware to begin mining. A widely decentralized network of users is one of the keys to making Zcash a success.
UPDATED Feb 2017: This Tutorial is still good for learning to mine Zcash with a CPU but you will want to use a GPU for the best results. Visit my new site for the new mining tutorials: https://www.zcashcommunity.com/mining
Please have a look and share with your friends!