Please see this Wikipedia article and this post of mine where I provide detailed explanation of Shatnez. For detailed Torah passages see Leviticus 19:19 and Deuteronomy 22:11
Here is a very simple method to identify Shatnez: rub two materials in question against each other. If you can see/hear/feel sparks (aka static electricity) - it is Shatnez. As usual with the Torah, everything genius is simple.