Allah the Almighty commands:
“We have sent It (the Quran) down on the night of Qadr. Do you know what the night of Qadr is? The night of Qadr is more valuable than a thousand months. The angels descend in it with all orders and by the permission of their Master for all kinds of affairs. Peace be within that night until the break of dawn.” (al-Qadr 97:1-5)
“Ha’. Mim. By the Clear Book! We have sent it down on a blessed night. We warned people (with It). Every determined decree is distributed on that night. We have decreed those; We only send messengers as grace of your Master. Surely, He is the All-Hearing, the All-Knowing.” (al-Dukhan 44:1-6)
As it can be seen from the verses above, the night of Qadr is a special time in various aspects.
1- It is the night in which the first verses of Quran was revealed to Messenger Muhammad (pbuh).
2- It is a specific time of the year where some decrees are distributed around the earth by the means of God’s messengers (angels).
People have been seeking this night because of its importance and a sign of respect to the divine book, the Quran. Because of the annual distribution of decrees, it is advised to pray more and ask Allah for forgiveness in this time of the year. However, we do not know any specific kind of worship to do in this night. When Aisha (wife of the Prophet) asked Muhammad about what to do in this night, the Messenger of Allah answered:
“Say: O God! You are the Forgiver, the Generous. You like forgiving. Forgive me too!” (Tirmidhi, Dawat/Blessings, 84)
About the last 10 days of Ramadan,
We know that the first verses of the Quran were revealed in the month of Ramadan. Allah decrees:
“The month of Ramadan in which was sent down the Quran (…)” (2:185)
When people asked the Messenger about the time of the night of Qadr, he said:
“I had been showed the time of the night of Qadr, but then I was caused to forget it. Seek it in the last ten days and the odd ones.” (Bukhari, Fadl’al-Laylat’al-Qadr/Virtue of the Night of Qadr, 2-3; Muslim, Siyam/Fast, 213)
Nobody can claim to know the exact time of that night, as the Prophet says that he was caused to forget it.
There is also one verse that Allah vows on ten nights.
“By the dawn! And the ten nights! And the even and the odd! And that night when it passes! Isn’t there an oath in this for those endowed with good sense?” (al-Fajr 89:1-5)
The Prophet used to seclude at the masjid in the last ten days of Ramadan. Using this information, most of the scholars inferred that these verses may refer to the last ten days of Ramadan which makes the previous hadith more meaningful.
Applying oneself to worship in the last days of Ramadan is one of the highly advised habits of our Prophet and was widely practiced in his time. Allah says about the people that sustain this habit:
“Do not have intercourse with your wives while you continue to stay for worship in mosques.” (al-Baqarah 2:187)
Please see also: http://en.wikipedia.org/wiki/I’tikaf
As conclusion, the night of Qadr is a truly special time of the year. However, we do not know its exact date, and there is no specific worship to perform on that night. The only thing advised to do is to pray more, ask Allah for forgiveness and seclude in mosques for certain times during the day if the chance is found. So long as we do not know the exact date of the night of Qadr, it is advised to practice these in the last ten days of Ramadan as an annual service of confession and redemption.