Clay is a resource used to craft different things in Myth of Empire. Most workbenches and many buildings require a decent amount to be built.
In Order to find some clay you need to look for clay nodes near any water (image below). The map contains a large amounts of clay ressources along rivers, lakes and the coast of the ocean. You will have to use your stone hammer to mine it. Take the hammer in your hands and start hitting a clay node to obtain clay.
If you want to increase the income of ressources from mining, you will have to craft better tools. Check out this guide about tools to be more efficient in Myth Of Empires.
To be able to craft the first parts of clay buildings you must reach level 26. Hit level 30 to craft all clay building parts. If you are planning to build a base out of clay you will need to collect a lot. Check out this building guide for beginners to learn the basics of building.