I'll go into more detail in my book, and Jamey Allen has written about this too: How does the Idar Oberstein agate get it's great colors?
A range of techniques is used, heat, chemicals, actual dyes, to make the natural occurring patterns of the stone stand out. It is considered the main reason why, once Idar-Oberstein started using Brazilian agate, their product became so very popular. The Brazilian stone took coloring methods very well.

Once Mr Weinz understood the type of things that interest me, he said: follow me..... And then we were in a small room, with a normal stove and there he had a pan of agate stones boiling away in sugar water. It would take several weeks for the stone to turn from grey to brown. And then he would put it in the oven underneath.

I asked him about some of the other colors, and he showed me a jar. Inside was the chemical mix they used to color agate as well. If I remember correctly, it was for making it green. he said that the mix in that jar was over 30 years old.