What to Do on Laylat al-Qadr
Question

How should we spend the night of Laylat al-Qadr? Is it by praying, reading Quran and the Sirah (Prophet’s biography), listening to sermons and lessons and celebrating that in the mosque?
Praise be to Allah.What Prophet Muhammad did in the last ten days of Ramadan
The Messenger of Allah (peace and blessings of Allah be upon him) used to strive hard in worship during the last ten nights of Ramadan as he did not do at other times, praying and reading Quran. 
Al-Bukhari and Muslim narrated from `Aishah (may Allah be pleased with her) that when the last ten days of Ramadan began, the Prophet (peace and blessings of Allah be upon him) would stay up at night, wake his family and tie his lower garment tight. According to Ahmad and Muslim: “he would strive hard in worship during the last ten nights of Ramadan as he did not do at other times.” 
What to do on Laylat al-Qadr
The Prophet (peace and blessings of Allah be upon him) urged us to spend the night of Laylat al-Qadr in prayer out of faith and in the hope of reward. 
Abu Hurayrah (may Allah be pleased with him) narrated that the Prophet (peace and blessings of Allah be upon him) said: “Whoever spends the night of Laylat al-Qadr in prayer out of faith and in the hope of reward, will be forgiven his previous sins.” 
This was narrated by the group apart from Ibn Majah. This hadith indicates that it is prescribed to stay up and spend this night in prayer. 
Best du`a for Laylat al-Qadr
One of the best du`a’s that can be recited on Laylat al-Qadr is that which the Prophet (peace and blessings of Allah be upon him) taught `Aishah (may Allah be pleased with her). It was narrated by al-Tirmidhi, who classed it as sahih, that `Aishah said: I said: “O Messenger of Allah, If I know which night is Laylat al-Qadr, what should I say?” He said: “Say: Allahumma innaka ‘afuwwun tuhibb al-‘afwa fa’fu ‘anni (O Allah, You are All-Forgiving and You love forgiveness so forgive me).” 
Singling out one night of Ramadan as Laylat al-Qadr 
With regard to singling out one night of Ramadan and regarding that as Laylat al-Qadr , this requires evidence. But the odd-numbered nights during the last ten nights are more likely than others, and the night of the twenty-seventh is more likely to be Laylat al-Qadr , because of the hadiths which indicate that. 
Can we celebrate Laylat al-Qadr
With regard to bid’ah (innovation), it is not permissible either in Ramadan or at other times. The Messenger of Allah (peace and blessings of Allah be upon him) said: “Whoever innovates anything in this matter of ours [Islam] that is not part of it will have it rejected.” And he said: “Whoever does any action that is not part of this matter of ours will have it rejected.” 
With regard to the celebrations that are held on some nights of Ramadan, we know of no basis for that. The best guidance is the guidance of Muhammad and the worst of matters are those which are innovated. 
And Allah knows best.