Abdullah ibn `Umar (may Allah be pleased with him and his father) reported that the Prophet (peace and blessings be upon him) said: "There are no days greater in the sight of Allah and in which righteous deeds are more beloved to Him than these ten days, so during this time recite a great deal of Tahlil (saying: 'there is no god but Allah'), Takbir and Tahmid." (Reported by Ahmad)

This video discusses the virtues of the 10 days and tips for gaining blessings