There are two kinds of schools of Indian philosophy, Astika and Nastika. Astikas accept the authority of the Vedas, whereas Nastikas reject the authority of the Vedas. The Astika schools are part of Hinduism, while the Nastika schools fall under the broader category of Dharmic faiths. Now there are six Astika schools: Samkhya, Yoga, Nyaya, Vaisheshika, Purva Mimamsa, and Vedanta. (They're all dead other than the Vedanta school, which encompasses most Hindus today as I discuss here.)
Because they accept the authority of the Vedas, these schools all believe in Yagnas, the law of Karma, the existence of the soul, the afterlife, reincarnation, and Moksha. But one thing they disagree on is on the existence of God and how to prove it. Two Astika schools are atheist or agnostic on the existence of God: Samkhya and Purva Mimamsa. I discuss their arguments on the subject here. The other four Astika schools, namely Yoga, Nyaya, Vaisheshika, and Vedanta, accept the existence of God. My question is, how do each of these four schools prove the existence of God?