There are three ways to attain moksha, so to speak, as if moksha was not there in the first place, in Hinduism.
1. Karma Yoga - Action without worrying about their fruits. Example: a soldier at the frontline fights and kills without worrying whether he will go to hell for that.
2. Bhakti Yoga- Surrendering oneself unto the Lord, lock, stock, and barrel. Eat, sleep, and breathe God, so to speak.
3. Jnana Yoga - The path of knowledge, the path of discrimination of what is real and unreal. Very difficult to follow.
If either of the three yogas are followed right, one can escape the web of cause and effect, so to speak.
One can escape the law of karma through the grace of God. It is not just accepting God but to live one's life pleasing to God.
Hinduism talks in the vyavaharika(empirical), and the paramarthika(absolute) sense.
All these yogas, and the striving for liberation exist in the empirical sense.
In the absolute sense, 'cause and effect' is not there, no one strives for liberation. There is no bondage, so where does liberation arise.
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According to tradition all the Upanishads were transmitted orally and at the end of the last Dvapara Yuga(3102 B.C.) written down by sage Vyasa.
More information can be had from wikipedia, the most neutral website that I could recommend.