It is common misperception that naastikaas are those who denied the existence of God - this cannot be, as even various aastika schools like the Saamkhya and the Mimaamsaa disputed the existence/utility of a creator God. As Manu rightly notes the naastikaas or the heterodox thinkers are those who questioned the authority of the Veda. They were particularly concerned about three issues : 1. the authority of the Veda concerning matters of the spirit, 2. the efficacy of Vedic sacrifices and 3. the supremacy of the Brahmin.
It should also be noted that schools like the Saamkhya or Yoga, though labeled orthodox weren't absolutely faithful to the Vedas or its teaching. They merely paid lip service to the Vedas and where their views agreed they were most eager to claim orthodox support. Nor did they really endorse Vedic sacrifices or the supremacy of the Brahmin - according to legend Kapila, the founder of the Saamkhya, himself vigorously opposed animal sacrifices. And for the Saamkhya and Yoga, the real teacher was a realized soul who need not necessarily be a Brahmin. But where they differed from the heterodox schools was that they didn't strongly come out and register their opposition. Instead where their views agreed with the orthodox tradition, they were quick to claim support and where it didn't, they just ignored it.
History records many movements opposed to orthodox religion. For our purpose we've chosen only three, which we consider the most prominent as they find constant mention in the polemical treatises of orthodox schools. They are Brhaspati's Lokaayata, Gautama Siddhartha's Bauddha (Buddhism) and Vardhamaana's Jainaa (Jainism). While original texts of the Lokaayatas are scarce, the latter two has left behind an enormously rich philosophical literature.
It might also be useful for us to note here a fundamental difference in worldview between these three heterodox streams and orthodox religion. As noted in our exposition of the basic texts of orthodox religion - the Vedas, the Upanishads, the Gita and the Dharma Shaastrams, orthodox religion considers phenomenal life (samsaara) as suffering and believes as the true meaning of life, a supersensible and supernatural reality which is totally beyond phenomenal experience. But in a practical attempt to reconcile samsaara with moksha, it recognizes as the four ends of life - wealth, desire, virtue and liberation -and advocates the four stages of the aashrama system as the means to gradually ascend from samsaara to moksha.
In contrast to this, the Lokaayatas totally reject spirituality and assert only artha (wealth) and kaama (desire) as the true ends of life. Simply put they are spiritual skeptics and outright hedonists. The Bauddhas and the Jainaas on the other hand, agrees with the orthodoxy that samsaara is suffering. But without any attempt at reconciliation they reject artha and kaama as evil and sinful and stress the importance of only dharma (virtue) and moksha (liberation from the cycle of rebirths).