Sunnah (Prophet's Example) in Performing Night Prayer
Question

                If a Muslim performs taraaweeh in a
      mosque, is it allowed for him to perform the night prayer at home?
      What is the Prophet's 
 (peace be upon him) manner in performing night prayer?
Praise be to Allah.If a Muslim performs Taraaweeh in
    congregation in the mosque, and wants to offer more prayers at home, he should pray a
    series of two-rak'ah prayers and should not repeat witr, because the Prophet 
 (Peace &
    Blessings of Allah be upon Him) said: 
    "There cannot be two witr prayers in one night." (Reported by Imaam Ahmad and
    others, and deemed saheeh in Saheeh al-Jaami', 7565).
    Umm Salamah reported that the Prophet 
 (Peace & Blessings of Allah be upon Him) used
    to pray two rak'ahs after witr. (Reported by al-Tirmidhi and others, al-Sunan 433).
    Al-Nawawi said: "The correct opinion is that he performed the two rak'ahs after witr
    sitting down, to demonstrate that this is permissible, and he did not do this all the
    time." (Tuhfat al-Ahwadhi Sharh Jaami' al-Tirmidhi).
    The sunnah is to make the last of one's night prayers an odd number of rak'ahs, as is
    reported (Saheeh al-Bukhaari, no. 943). But if he has already prayed with the imaam, and
    wants to perform more prayers on his own and has time to do so - especially in the winter
    - he should do as is outlined above.
    As regards the number of rak'ahs to be performed in the night prayers, the Sunnah is to
    perform no more than eleven rak'ahs, because of the hadeeth narrated by 'Aa'ishah may
    Allaah be pleased with her, who said:
    ". . . He never used to pray more than eleven rak'ahs, in Ramadan or at any other
    time . . ." (Reported by al-Bukhaari, no. 1874).
    The best way to perform the night prayer is to pray two by two (rak'ahs), and to separate
    the two even rak'ahs of witr from the one rak'ah (i.e., not to join the three rak'ahs of
    witr). The evidence for this is the hadeeth of Ibn 'Umar (may Allaah be pleased with them
    both), who said: "The Prophet 
 (Peace & Blessings of Allah be upon Him) used to
    perform the night prayers two by two (rak'ahs), then he would end with a single
    rak'ah." (Reported by al-Bukhaari, al-Fath, no. 940).
    This is the best-known way of performing the night prayers according to the Sunnah of the
    Prophet 
 (Peace & Blessings of Allah be upon Him); other ways are also known.