Hadrat Abu Qataadah narrated that the Beloved Prophet the Rasoolallah (PBUH) said:

I hope from Allah that {in His consideration} The day of Aashura {Tenth day of Muharram Ul Haram} will atone for the previous {the past year}. {Tirmidhi}

Hadrat Ibn ‘Abbas has narrated that the Beloved of Allah, Muhammad (PBUH) said:

The person who fasts on Aashura {tenth day} of Muharram will be given Thawab {rewards} of 10,000 angels and Thawab of 10,000 people who perform Hajj and ‘Umrah. Any one who strokes affectionately an orphan’s head, Allah will increase his station in Paradise by the number of hair on the orphan’s head and any one who feeds a fasting True Believer at Iftar {breaking the fast} it would be considered as if he fed at Iftar all the Ummah of Hadrat Rasoolallah (PBUH), till their stomachs are full.

The companions {may Allah be pleased with them all} respectfully submitted O Rasoolallah (PBUH) Allah has given to the 10th day of Muharram, more greatness than all other days. He (PBUH) replied Yes. Allah created the heavens and the earths on the day of ‘Aashurah, created mountains on the day of ‘Aashurah, created his pen {Qalam} on the day of ‘Aashurah, and the Lauh Mahfooz {The Guarded Tablet} on the day of ‘Aashurah, created Adam on the day of ‘Aashurah and gave him entrance into Paradise on the day of ‘Aashurah, Hadrat Ibraheem was born on the day of ‘Aashurah, and the Pharoah {Fir’aun} was drowned on the day of ‘Aashurah, and Allaah removed from Hadrat Ayyub his affliction, and Allaah accepted the Taubah {repentance} of Hadrat Adam on the day of ‘Aashurah and Allaah forgave the mistake of Hadrat Dawood on the day of ‘Aashurah and Hadrat ‘Isa was born on the day of ‘Aashurah, and the Day of Judgment will form on the day of ‘Aashurah.
{Ghuniyatuttalibeen - Tarteeb Shareef pages 756, 757}

Hadrat Ibne Abbas has narrated that the Beloved of Allah, Muhammad (PBUH) said:

The person who fasts on the day of ‘Aashurah in Muharram, Allah will write for him worship of 60 years and in this worship is included fasts during days and nights in worship. Any one who performs a Ghusl {head shower} on the day of ‘Aashurah he will not be afflicted with any sickness except the sickness which leads to his pre ordained death and anyone who applies Soormah {Collyrium} to his eyes, his eyes will not suffer any pain during the entire year and anyone who visits a sick person on the day of ‘Aashurah it would be as if he visited all the progeny of Hadrat Adam. Anyone who offers a drink of water once on the day of ‘Aashurah it would be considered that he did not disobey his Lord for even one batting of an eye lash. Anyone who performs on the day of ‘Aashurah 4 Raka’h of Salat and recites after Surah Al Fatihah, Surah Al Ikhlas 50 times, Allah will forgive his sins of the past 50 years as well as his sins of the next 50 years and Allah will reward him with 1,000 Palaces in a group above the Noor {light}.

Hadrat Abu Hurairah has narrated that the Beloved of Allah, Prophet Muhammad (PBUH) said:

The 4 Raka’h should be performed with 2 Salams and in each Raka’ah recite Surah Al Fatihah once and Surah Al Zilzaal once, and Surah Al Kaafiroon once, and Surah Al Ikhlas once and after the completion of the Salah recite Salaatul Nabi {Durood} upon the Beloved of Allah, Prophet Muhammad 70 times.

{Ghuniyatuttalibeen - Tarteeb Shareef pages 758-756}