Do lots of dhikr!
“Therefore remember Me (by praying, glorifying, etc.). I will remember you”[al-Baqarah 2:152]
The Prophet (peace and blessings of Allaah be upon him) commanded us to recite a lot of Tasbeeh (“Subhan-Allaah”), Tahmeed (“Al-hamdu Lillaah”) and Takbeer (“Allaahu akbar”) during this time. ‘Abdullaah ibn ‘Umar (may Allaah be pleased with him and his father) reported that the Prophet (peace and blessings of Allaah be upon him) said: “There are no days greater in the sight of Allaah and in which righteous deeds are more beloved to Him than these ten days, so during this time recite a great deal of Tahleel (“La ilaaha ill-Allaah”), Takbeer and Tahmeed.”
(Reported by Ahmad, 7/224; Ahmad Shaakir stated that it is saheeh).
source: Islam qa