He studied under a variety of philosophers, picking gems of thought up from each one. Deciding the saying "NO" was defining yourself, and saying "yes" was allowing someone else to define you. Therefore we must be slow to say yes.
His approach to Logic was this:
"Zeno said that there were four stages in the process leading to true knowledge, which he illustrated with the example of the flat, extended hand, and the gradual closing of the fist:
Zeno stretched out his fingers, and showed the palm of his hand, – "Perception," – he said, – "is a thing like this."- Then, when he had closed his fingers a little, – "Assent is like this." – Afterwards, when he had completely closed his hand, and showed his fist, that, he said, was Comprehension. From which simile he also gave that state a new name, calling it katalepsis (κατάληψις). But when he brought his left hand against his right, and with it took a firm and tight hold of his fist: – "Knowledge" – he said, was of that character; and that was what none but a wise person possessed."
The nature of the universe was that God was like a divine fire foreseeing all and working through all through eternity. And as fire has different forms and life, the universe will regularly go through change as well.
He taught that people should control their passions and by doing so they will achieve wisdom and knowledge. By use of meditation one can develop and indifference to pain and pleasure and thus apply oneself to gaining wisdom. Wise people should have children. He believed that "If one is self-aware, one is also aware of others and, further, recognizes that it is in simplicity that true contentment may be found".
Sources:
The philosophy book
Wikipedia
Philosophy basics
Crystal Links.
Ancient History.