jaloysius, you seem to be misunderstanding the problem a little. Imagine you're sitting at a workbench and all you have are Nand gates. Your goal is to implement a Not gate. How would you build a Not gate out of the parts (Nand) that you have?
Once you build a Not gate, now you have two parts on the workbench: Nand and Not. How could you build the next chip, And, out of the parts you have (Nand and Not)?