How do I start getting sentient goods.
That link to elvengems is the best, it will get you through the chapter well.
The short answer to your question is, sentient goods can be produced in a level 24 manufactory. Your boosted sentient good will be your regular boosted good +1. So, if you are boosted in steel, you will want to build a planks manufactory to level 24 and begin producing the Tree Gum as your boosted sentient good.
If boosted in marble, build steel
If boosted in Planks, build marble
And the same system applies for tier 2 and 3 of your goods.